What is the difference between Moris Minors/Austin Mini's Mini Coopers and whatever else thee is in similar cars.

If you're asking what's the difference between similar Austins and Morrises, it depends on the model.
In the case of the Mini and Mini-Cooper variants, not much - truly badge engineering only. If you take the grill and badges off, you'd have to be a real nerd to say which was which.
If you're asking how Mini Coopers differ from Minis, I'd advise you to use the interent to find articles. The Wikipedia entries aren't bad, though I'm not usually a fan.

Going back to the Austin vs Morris differences, it's generally true to say that Austins were usually the baser models, Morris a little more upmarket, then Riley and Wolseley, with MG being the sporting variants. That was pretty much the case for BMC in the UK, but I know they used different badges on export models so that may not have been true over here (USA).

If you have a Mini, Interested in getting one or just interested, you might check out the information that can be found here:
How to ID your Mini

The Morris Minor is a much larger car....like the Chevy Caprice was to the Chevette. As far as the Austin Mini / Morris Mini...the name badge on the nose is probably the biggest noticable difference. A Mini Cooper is to a Mini what a Shelby Mustang is to a plain Mustang. That's the short explanation. Hope it helps a little.

I assumed (dangerous, I know) that he meant Morris Mini-Minors, which is what the Mini was called originally, if it wasn't an Austin Seven, that is!