There are many formats for writing to a CD or DVD. Some lock the disk entirely, some lock each "batch" of content so you can't modify an old batch but can still add new content to the disk if there is free space, and some treat the whole disk like a flash drive. Depending on what software you are using to write to the disk, selecting that option may appear when you first load a blank disk, at the time you write the content to the disk, or when you go to eject the disk. Some software does a better job than others at explaining the choices. If you are never getting any options for the format to use, let us know what software you are using and what you are trying to store (e.g., data, music, video).
One other thing to check is the type of drive you are using. A "rewrite"- capable drive can treat rewritable media like a flash drive, erasing and reusing the disk. If it is a rewritable drive, it should say so, typically on the edge of the tray that is visible when the drive is open. You will get formatting options that will not appear with a standard drive. With a standard drive, you will be limited to choices that either lock the disk at the end of the session or lock the content but leave any free space available. Using rewritable media won't buy you anything if the drive is not a rewritable drive.
I'm not using any specific software, I presume the write routines are part of Windows 7. They were never locked between sessions.
Formatting options offered are UDF 2.01 (Default - which is current); UDF 1.5; UDF 2.00 and UDF 2.50 in 2048-byte chunks. Perhaps a change of file-system may cure the problem??
Disc was a good quality Verbatim CD-RW rewritable. The disc has 592,531,451 bytes written, ( just over 565Mbytes), hardly the 700M the disc is supposed to support.
The drive is a Lightscribe AD-7261S ATA, marked DVD [RW] Multi-recorder RDL on the tray.
It stumbled when about to write the second file (.JPG) in the (probably)13th session. The file wouldn't have taken it over the 700M limit.
(FWIW the other writer on the system is an unknown make, ATAPI iHAS 324 Y-ATA device marked DVD+RDL DVD Multi-Record).
Perhaps someone can recommend good software, free or paid for, which would get me to where I need to be ... otherwise I'm going to end up having to do these scratch discs in multi-session CD-R which is rather inconvenient.
There are a number of different aspects that I'll try to address separately and then get back to your problem at the end.
Your optical drives: I could not determine whether the two drives you mentioned are "rewritable" drives. If they are, the tray will contain a logo "Compact disc ReWritable". The "Multi-Record" could just refer to the fact that the drive handles CDs, DVDs, and different types of media. My understanding is that the RW designation on the drive just means that the drive will work with rewritable media, not necessarily that the drive will perform rewriting (which requires an erasure process that non-rewritable drives do not have). The rewritable media tends to be more expensive so if your drives are not rewritable drives, it's just a waste of money. But if my understanding is correct, RW media is compatible with your drives so that should not be an issue contributing to your problem.
If your drives are not rewritable drives, you will never see options that work only with rewritable drives and rewritable media. Those options allow you to treat the disk like a flash drive and read and write without locking anything on the disk. It doesn't sound like that is the problem you're experiencing.
When you say the formatting options offered... and then talk about UDF versions, it sounds like you've done some digging in the weeds. Windows doesn't present that as the main options users see when you insert a disk. My understanding is that the UDF versions are cumulative; each new version just added to what was already there in order to handle new kinds of media and capabilities. Normally, you wouldn't change that and if you found a place to do that, leave it set to the highest number available. It generally is not a good idea to micro-manage the formatting. Even if you were successful, you would likely run into problems trying to use the disk afterwards.
When you insert a blank disk, you typically get an AutoPlay menu that covers your basic options for what you can do with the disk. If you are not getting that, look in Control Panel/ Hardware and Sound/ AutoPlay. You may have disabled AutoPlay by previously telling it to always handle blank disks a default way.
There are differences depending on what you want to store on the disk (data, audio, video, games, media for a specific type of player, etc.). This choice affects how information is stored on the disk and how the disk is locked. Make sure you select the appropriate content type.
If you use a format for data or mixed content, you should be presented with a choice of how to lock the disk. This might be either at the time you initialize the disk or when Windows finalizes the writing before ejecting the disk. You may also get a choice concerning whether the disk should be readable on any computer or just continued use on yours. At a minimum, you should get to select whether to lock the disk so no further writing is possible, or lock the session and leave any remaining space available. Do you get that option?
You do need to be aware of the actual size vs. the size on disk of what you are trying to write. If you are writing thousands of tiny files, they can occupy substantially more space on the disk than the raw file size. In most cases, you will get a warning if you try to write more than what will fit on the disk. However, I've seen Windows get fooled. That can lead to ruined disks or Windows Explorer (or the computer) hanging.
In terms of special software, you don't necessarily need any. What comes built into Windows 7 will handle most needs.
The media's rated capacity is not necessarily a reliable number for every use. It is really a "nominal" raw maximum capacity before formatting and overhead, just like on a hard disk. Depending on how you format and use the disk, you may get less. After you initialize the disk, right click on it and check its Properties. That will tell you exactly how much space there is on the disk.
Be aware that optical media, especially the cheap stuff, has a not-insignificant failure rate. Through no fault of your hardware and software, some percentage of discs will fail before completing the desired write operation. If you are storing important stuff, it is not a bad idea to create a backup copy of the disk. There can also be problems with dust or other contaminants inside the drive that can interfere with successful writing or reading. If you use optical media, you will have scratch disks.
That will only work if the drive is a rewritable drive. Only those drives have the erase function. Rewriting is only possible with RW media (contains a special layer that can be erased), but using that media won't let you rewrite the disks if it is not performed on a rewritable drive. From what I could research, it doesn't look like the drives you mentioned are rewritable drives, but if they are, they will have the "compact Disc ReWritable" logo on the drawer.
BTW, rewritable disks are not a good substitute for a pen drive. You can reuse the disk, but only a limited number of times. They aren't designed for constant rewriting. They are more appropriate for something like a rolling backup, where the content gets replaced over time, maybe a number of times, but not on a continuous basis for the same area of the disk.
Actually, pen drives are not a good substitute, either, for a hard disk for an "active" memory process. The simple flash memory configuration used in them is designed for "storage" type reuse, not active, repetitive writing. Their life can be as low as a few thousand write cycles, which can last a very long time if it is used for the appropriate application. SSDs don't suffer from the same limitation (they are not just a collection of flash memory, they are designed to be used like a hard disk).