Samba and Bossa Nova: What is the difference?

It is not easy to describe the difference between the two in words. It is much easier to compare examples of samba and bossa nova by listening to them.

Samba as a genre probably originates in the early 20th century and while based on African drum playing (which was kept alive much more amongst Brazilian slaves than it was in the States) also derives much of its melodic and harmonic complexity from Portuguese fado and other styles. It is not, and never has been, a fixed style of music and is in constant development and has both been an influence on and has been influenced by music from other cultures.

There is quite a good article on Samba here: http://en.wikipedia.org/wiki/Samba which will, at least, serve as a starting point in studying the music.

The name 'bossa nova' comes from the Portuguese meaning 'new trend'. In Brazil, 'bossa' has the additional connotation of something done with 'charm' or 'flair', so 'new style' might be a more apt translation. Bossa nova is an offshoot of samba popularised (and, one could say, 'invented') by João Gilberto, Vinicius de Moraes and Antônio Carlos Jobim. It relies less on drum rhythms and more on the guitar. On the whole it tends to be quieter, more introspective and much more harmonically complicated than samba. The song, "Girl From Ipanema", was one of the earliest and is still one of the most popular examples of Bossa Nova and Jobim's "Desafinado" exemplifies the striking melodic and harmonic innovations.

There is more about Bossa Nova here: http://en.wikipedia.org/wiki/Bossa_nova. Again, Wikipedia should be taken as a starting point for further research.