Here is the Wikipedia article on musical genres. Musical forms are a little clearer. Here is the Wikipedia article. For the sake of simplicity, I'm going to go with these definitions: musical forms are those structural aspects that we usually parse out with letters. A piece in ABA form has an opening idea or theme, then it goes to a different one, then returns to the first one. Musical genres, on the other hand, are described in more concrete ways as the feeling of a specific genre, such as a waltz, is defined by the meter (3/4) and tempo. A concerto, which may or may not use the classical forms typical of a concerto, is defined by the opposition or contrast between a solo instrument such as the violin, and a larger body of instruments, such as an orchestra. There are innumerable genres and sub-genres and composers may blend them together to achieve unique effects. Chopin's Nocturne in G minor has been described as combining a mazurka rhythm with the nocturne and also using religioso passages.
Here is an easy way to distinguish form from genre. The baroque suite was comprised of a number of different dances sometimes preceded by a prelude. The form of these dances was usually the same: AABB or two distinct sections, each repeated. Harmonically the first section begins with tonic harmony and the second section ends with tonic harmony making for a tidy conclusion. In a major key, the first section usually ends with dominant harmony and the second section works its way back to the tonic. In a minor key, the first section often modulates to the relative major--the major key that has the same number of sharps or flats as the minor tonic. So if the form is basically the same for all these dances, what distinguishes one from the other? The answer is genre. Let's look at Bach's Cello Suite No. 1 for an example. Here is the courante, which is in two sections, each repeated and the first section ends with a cadence on the dominant. It is also in 3/4 meter.
Immediately following this is the sarabande which is in the same key, G major, the same meter, 3/4, also in two sections of which the first cadences on the dominant.
So the two movements share the same form. Why do they sound so different? The answer is that a courante is a different genre than a sarabande. The courante, a dance that divides into two sub-genres, is quicker than a sarabande. The two types are the French and the Italian. This is an Italian type that is the quicker of the two and is rhythmically lively with running passages. The sarabande, a Spanish dance, is much slower and, in contrast to the courante, stresses the second beat. Immediately after the sarabande are a pair of dances with, again, the same form: two sections, the first ending on the dominant and also in 3/4. These are the two minuets. The tempo is slower than the courante and the rhythms are simpler and more graceful. The first minuet, AABB with the first section ending on the dominant, is followed by the second minuet, which is in the parallel minor--the minor key with the same tonic as the major of the first minuet (G major, then G minor). Then, the first minuet returns, but this time without the repeats.
All three dances are roughly in the same form with the same key, same modulations, same sectional layout and same time signature. But they sound so different from one another that they can immediately follow one another in the suite without the listener becoming bored. The reason is that they are of very different genres. The dance genres are responsible for the different tempos and the internal rhythmic structure.
One of the things that was largely lost in the move towards musical modernism was this repertoire of genres that composers could make use of. They are still available, of course, but composers have usually avoided them in the last hundred years.