They are similar but not exactly the same. I typically do rhythm squats at half or 1/4 squat position with the emphasis on turning the bar around very quickly.
I have done speed squats as you mentioned. That protocol is straight out of old soviet speed training manuals. I liked it but I always found it difficult to time the reps with reasonable accuracy. Also, I found it difficult to standardize depth at the higher speeds. You could use a box or medball but when athletes are racing against the clock there's always the temptation to cut the ROM short.