That's almost true.
The original 400K floppy drives in both the Macintoshes and the Lisas were identical. They were usually, but not always Sony units.
The difference in drives between Mac's and Lisa's came around the time of either the 512K or the Plus - i.e. the first of those to introduce double sided floppy drives.
The Lisa doesn't always auto-eject the floppy on power off, but this is a function of software (either the ROM or the last OS running), and not the drives themselves. If you run Lisa Office System, it will eject floppy media before shutting down, for example. The Lisa infact does have a software-eject feature just like the Mac 128.
You can always prevent a Lisa from booting off a floppy that's inserted into the drive by holding down either the mouse button or a key on power up. This will bypass the PRAM setting that says "always boot from floppy" and present the Lisa's standard boot menu.
If you can find an external floppy meant to be used with the original Mac 128 (these were required due to all the swapping you'd have to do otherwise), the drive inside those cases will work with Lisas. (So will the drive inside a Mac 128, but I certainly wouldn't want to sacrifice a Mac 128 to get a Lisa working as 128's are rare too, and a working 128 is a thing to treasure.)
Note that a "Mac XL" is really a Lisa. The term "Mac XL" is misleading since it refers to many kinds of Lisa 2's. Apple sold these as XL's by bundling MacWorks when they decided to no longer support the Lisa Office System software.
Some of these XL's were modified with a screen modification kit, so that they'd have square pixels instead of the 2:3 aspect ratio pixels. Lisas modified in this way could no longer run Lisa Office System (nor Xenix) and were stuck with only being able to run MacWorks variants. see http://www.folklore.org/StoryView.py?project=Macintosh&story=Square_Dots.txt
and http://lisafaq.sunder.net/lisafaq-hw-rom_versions.html
XL stood for either eX-Lisa, or Extra Large (since a "Mac" XL had either 512K or 1M of memory while the Mac only had 128, and the XL also had a larger screen.)
(The nice thing about MacWorks is that you can run it without a hard drive, though this makes for a pretty lame Lisa, especially since you have to swap floppies just to boot, and then swap floppies some more to copy stuff from one disk to another. Kind of cripples the Lisa to being a little bit more useful than a Mac 128 - although I suppose if you can find the ancient ram disk program that might make things a lot better.)
An XL could be a Lisa 2, or a 2/5 or a 2/10. Either of those configs could have the screen modification kit, or they might have a stock ROM such as the H or F. The only thing the "XL" label means is that it came bundled with MacWorks. You could always buy MacWorks and turn your Lisa 2 into an XL.
(If you bought certain versions of MacWorks Plus, specifically those with hardware accelerators, you would also would no longer be able to run Lisa Office System.)
Modifying the Lisa's I/O ROM to support 800K floppies will also break usability with Lisa Office System. (I think - I don't know for sure since my Lisas have the stock 400K I/O ROM.)
Sometimes people refer to Lisa 2/10's as XL's, which also isn't quite right.
There is a difference in the whole entire I/O board between Lisa 2's and Lisa 2/10's. - the 10's have a slightly different I/O board that doesn't require the lite (sometimes called pepsi) card, and has the whole IWM on a single chip as opposed to several chips. It also has an I/O ROM version of 88 instead of A8, which is another way to identify them without actually looking.
A big danger with the old I/O boards (the A8's) is if they still have the 4-pack of NiCAD batteries - these have almost all leaked and in doing so have corroded the I/O board in the process. If yours has the pack still attached, immediately remove it!