Basically, I have a legacy Pi and Ubuntu MATE for RPi says it's for RPi 2.
Will software designed for RPi 2 boot / run on legacy Pi? Are there big incompatibilities?
I think the closest thing we have to a previous version of this quesion is this:
And the same logic applies to MATE. The reason there's a pile of distros for the Pi 2 is that most of the big names including Ubuntu already had ARMv7 versions, since ARMv7 is much more common beyond the pi than ARMv6. But those won't run on A/B/+ models.
Although some of them appear to be made just for the pi, this is probably not entirely true. On the one hand, no matter what, a pi compatible distro does require a custom kernel. On the other, compiling the kernel is only a tiny speck of a task in relation to the thousands of packages that make up a distro, all of which must be maintained over time and may need the equivalent of (several) full time hours to do. For the big mainstream distros, this is spread out over a large number of packagers who are responsible only for a few packages each and can therefore probably take care of things in an occasional evening. And/or they pay people (related).
I would guess that MATE is an elaborated version of something like this;1 most of the packages come straight from the pre-existing Ubuntu ARMv7 (which I think much of that may come straight from the pre-existing Debian).
1. There's a note there observing that after I wrote that someone in fact released a Fedora "Pi Remix" which has all the work done for you. This is what the original Raspbian was -- one volunteer who put together a precompiled pi kernel with an existing Debian ARMv6 distro. Most of the other brands don't have one; Debian supports a wider range of hardware out of the box than anyone else.