Salsa is much more than just a "sloppy Mambo". To simply take your Mambo and loosen it up is not going to make Salsa, any more than taking classical music and making it sloppy word turn it into jazz. Salsa has a feel and a technique all its own.
For starters, as Mambo Queen mentioned, Salsa typically breaks on 1, or sometimes 3. Some people even shift between breaking on 1 and 3 throughout a dance. But most people think of the basic Salsa rhythm as QQS -- with the break on the 1.
Salsa movements in general are very rotational and fluid, unlike the sharp, angular directional changes seen in Mambo and other ballroom-style Latin dances. This makes leading more natural, as it requires less and/or fewer shifts of weight connection from push to pull or vice-versa.
That's not to say that there's no connection at all, but the Salsa connection has an entirely different feel. I've heard it described as a "tethered" connection, meaning that it's relatively loose when the rope has slack, but it tightens up as slack runs out. In other words, you'll typically get a pull connection at the full extension of a line or extended position, but it occurs naturally, and doesn't need to be manufactured by unnecessary arm tone.
In terms of the repertoire, yes, there are many movements that the two dances have in common... the basic action, the cross-body lead, etc. But there are definitely aspects of the repertoires of each that very much sets them apart. For example, I wouldn't be caught dead in a Salsa club in L.A. doing a crossover break. But Mambo wouldn't be Mambo if you didn't have at least a few crossover actions involved. Salsa moves are characterized by continuous spins & turns, numerous head loops, cross-hand connections and hand-to-body connections. The salsa repertoire is formed by social and nightclub dancers, and is therefore sexy and intimate. Mambo, in contrast, is typically more showy and technique-driven, and the syllabus reflects that.
All of these observations are generalizations. There is not one description I've given of one that cannot be applied to the other to some degree (other than no crossovers in Salsa, but even that might be different in other areas of the world for all I know). Mambo can certainly be fluid or sexy, and Salsa does throw in some interesting complicated weight connections now and again. Moreover, Mambo as danced at the ballroom competitions is slowly being influenced more and more by Salsa, so that the line between the two is much more blurred now than ever before. Still, my point remains that there are very distinct differences between the two styles, and you son't really understand them unless you take the time to study them both in depth.
Regards,
Jonathan Atkinson