There are technical and philosophical differences.
In Cross-body (on 1 and on 2) you “stake out” a part of the dance floor (your slot) and stick to it; in Cuban the dance floor is more of a shared resource – somewhat by necessity as you dance around your partner (and even more so in Rueda de Casino, the circular partner-swapping form).
Cuban is often seen as a little more egalitarian in that the man does more dancing rather than just leading; many Cuban dancers feel more as though they are dancing more for their partner rather than showing off and dancing for the whole room as they feel is the case in Cross-body.
There are 3 basic holds/steps in Cuban – the “Son” step which is essentially the same as an on 1 basic, the back basic (the default Cuban basic) in which you step back with each foot rather than forward and back, and the Casino step (sometimes incorrectly referred to as the guapea step) which is an out and in step in an open hold. The Dile que No, which is the transition from close hold to Casino (and ends many Cuban moves) is also fundamental to Cuban.
Cuban Salsa also encompasses other traditional Afro-Cuban dance forms, and you can break out from Salsa for a few bars and dance Afro-Cuban Rumba, Mambo, Reggaeton, or pretty much anything that fits the beat.
I would just add the difference between on1 and on2. It basically refers to the main beat where the change in direction of the foot movement is seen by the lead. On1 the direction changes comes after the 1 (step forward on the 1 and back on 2 with the left foot) whereas in on2 it comes after the 2 (change direction after stepping forward on the 2). Watch some videos on you tube to clear a much better idea visually.
Salsa cubana dance in a circle where directions doesn’t matter, while salsa on 1 (often known as LA style) and salsa on 2 (often known as mambo or N.Y Style) dances on a “line”. On1 and On2 is when the leader gives a lead. I would say on1 and on2 is more similar than salsa cubana.
All styles are fun.
Cuban salsa is circular, crossbody (on1, on2) are linear. Circular meaning that most of the time, the lady is going around the man who stays pretty much in place and whilst in crossbody salsa the ladies may move a lot (and the man gets out of the way), moving in a line is easier than in a curve.
Cuban step is with the whole foot, crossbody tends to go for ball-heel stepping.
Cuban body motion is more sideways and that doesn’t work very well if you are moving more front and back.
Cuban dancers tend to love timba, which is a version of salsa with funk, hiphop influences. Crossbody salsa tends to be either, well, salsa and more latin jazz kind of stuff. Some of the cuban people round where I live have actually said that salsa is the music of their parents (ie. old people) and timba is the way to go. To each their own.
To me it seems that if a couple is dancing cuban, the lady is mainly running around the man who is doing all kinds of tricking. In crossbody salsa, the follower’s life is way more complicated.
To me it looks like the man does almost all of the dancing and that’s not egalitarian. I know many ladies who started with cuban and got bored with it as they don’t get to do anything. I also know many ladies that want to stick with cuban so that they don’t have to think and just go with it. If a crossbody salsa leader isn’t dancing, well, it’s his fault. The dance does not prevent it. Puppet mastery isn’t dancing.
A lot of how much the follower can do depends on the choice of figures (simple, complicated, pauses, one hand/two hands held/needed, how much the follower has to move around) — this doesn’t depend so much on cuban/crossbody but there certainly are things that are done more often in A than B. But the leader can affect that.
Very difficult to explain with words, except for the counts and steps, but there’s so much mor to a style of dance than those. I would suggest searching them on YouTube. Watch 5-10 videos of each style and you should start to get a feel for them. Steps and timing aside, the feel is what’s important.