They are fairly different. Yes, the players often play around the beat rather than playing it exactly, but the rhythmic concepts of Afro-Cuban, Jazz, and Brazilian music are pretty far apart.IMO jazz, Afro Cuban(and some Brazillian) have more in common than one may expect. In Latin music the Cuban Salsa sound is played much differently than the main land, in the sense that the pulse is not rigid in much the same way that the Jazz swing is not a rigid subdivision.
Jazz and Brazilian might be closest, but Afro-Cuban music is entirely different.
Mexican Salsa?? Whenever I work with Mexican musicians they bemoan the fact that PR has some great music, Cuba has great music, and they have mariachi! The only salsa you find in Mexico is the food!On the other hand the Mexican salsa is known for a very precise clave no cross rhythms.
I think you're getting mixed up. Xavier Cugat is really the person that many credit with bringing Afro-Cuban music to the US in the early 30s. Cole Porter's Begin the Beguine was written after seeing Cugat play at the Waldorf in NYC.Much of modern jazz can be traced back to Dizzie Gillespie, who sort of rescued the sound by importing fresh Afro Cuban elements, so they aren't all that distinct.
You're thinking of the 1940s, when Dizzy took Afro-Cuban rhythms and fused them with jazz, really starting Afro-Cuban Jazz. Afro-Cuban music and Latin jazz were already popular musical styles at the time. Songs like Mantecca are great songs, but they are more jazz than Afro-Cuban.
As far as Modern Jazz, Dizzy was involved with Bebop, which is considered one of the first Modern jazz styles, but you didn't see him much in other Modern Jazz styles. He had shifted to Afro-Cuban Jazz, and then moved back into a blend of trad jazz, Be bop, and Afro-Cuban Jazz. I don't think there were many recordings of him playing modal tunes, post bop, free, et cetera.