@johnweiss , this is open to debate. In branding you have 3 classes, luxury, standard, and budget. I think you have identified the 3 classes in audio that correspond..
Generally these categories differ by SQ and supposedly by price. I think of budget as boom boxes, low quality headphones, speakers made of low quality plastic, etc.
I think of midfi as gear that sounds better than budget and is sometimes found in big box retailers such as receivers, CD players, and the type of speakers that sound good, but not as good as reference class speakers you would find in a store that specializes in audio equipment.
High end gear is made of high quality parts (hopefully), sounds less like a bad recording and more like what the engineer heard in the studio. Sometimes gear is priced accordingly and sometimes budget or midfi gear ends up sounding closer to the high end category. That is a NEW category often referred to as "giant killer". Most members here like "giant killers" when they can find it. See this thread for examples: