'Foot rise' is a rise resulting from raising oneself onto the balls of the feet. 'Leg rise' is a result a full or partial straightening of the leg when commencing from a compressed or (bent-leg) position. In theory it is possible to use either type of rise independently or to use both simultaneously, although typically throughout much of ballroom they are used together, which is one of the reasons it is difficult to understand them as separate topics.
As for 'body rise' it is a myth or at least a misnomer! And a nasty one that seems to confuse even many of the highest level professionals. Most teachers of any subject (dance included) are as mad as bloody hatters and think they are doing all sorts of things they aren't when they undertake whatever it is they are trying to teach you and that they AREN'T doing all sorts of things they clearly ARE if you watch them! As a student of anything, one needs to learn to filter the good advice they give you from their years of experience and expert ability from the nonsense they sprout out of tradition or confusion....not that that's always easy but total physical impossibility is always a good clue!!
'Body rise', if you interpret it literally CANNOT exist because, as you will soon notice if you stand in front of a mirror, it is impossible to lengthen the region of your spine from your coccyx to your skull short of lying down for 8 hours sleep (which apparently makes you grow about 1 cm or so, which gravity then robs back off you throughout the day as your spine recompresses), going into zero-gravity for a while (same principal) or perhaps the employment of some sort of medieval torture device such as the rack! The best you will manage, if you try, will be to shrug your shoulders (which is clearly not what is intended). Given the impracticalities of the formerly mentioned techniques during a bar of even the slowest foxtrot, then if you think logically about it, it can't have anything to do with your body or trunk as the name suggests.
Given that you can only rise using your feet or legs then, 'body rise' MUST be the employment of one or the other or both of these or else a complete figment of the imagination, perpetrated by generation after generation of dance instructor.
Alex Moore, in Moore (2005)* describes 'body rise' as a bracing of the leg muscles, in as much as I can gather, which, by no co-incidence, is exactly what ‘leg rise' is!!
Rises termed ‘Body rise', depending on whether taken on a heel turn or on a simple backwards walk must be ‘leg rise' or perhaps on the latter, a combination of ‘foot' and ‘leg rise' and if you examine dancers, this is indeed what they appear to be doing. I know it's what I do and what my teachers actually do, despite the fact that some of them keep insisting I should spontaneously add and retract a few centimetres from my spine as they believe they have the mysterious and magical ability to do. I would pay to see that! Some people may tense the muscles of their trunk or other muscles of their body as some people here have claimed….that's fine…if it works to put you in the right frame of mind, I would say, do it by all means, each to his/her own, but be aware, it won't make your spine any longer!!!!
Thus, ‘body rise' is a redundant term!!!
Q.E.D.
* Moore, A. (2005). Ballroom Dancing. A & C Black Publishers Ltd., London., pp 20-24.