What are the differences??

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JackG has pretty much covered this, but I'll add what I've gleaned from my own reading: BJJ originally comes from judo, however, at the time (early 20th century) 'judo' was not the only term in use. Indeed, some still referred to it as 'Kano ju-jitsu' at the time, given that it was still a comparatively new style (founded in 1880 something, I think).

Gast*ão Gracie was a Brazilian diplomat, who helped out a Japanese individual name Mitsuyo Maeda, who was looking to establish a Japanese colony in Brazil. To show his gratitude, Maeda - who also happened to be an experienced judoka - offered to teach Gracie's son, Carlos. Maeda also had a background in various jujitsu styles, and as mentioned, the terms 'judo' and 'ju-jitsu' were not yet clearly delineated.

Carlos studied under Maeda for several years (there seems to be some debate about just how long, but in The Gracie Way, it states it was from the age of fifteen to twenty-one), before Maeda left the area. Carlos had learned enough that he felt ready to open his own academy in 1925, where he taught what he called 'jiu-jitsu' (Maeda most likely still referred to his judo as ju-jitsu, so that's unsurprising).

Another thing worth noting is that when Maeda came to study under Kano, judo was undergoing a focus on groundwork (or newaza, if you prefer), due to the school's first major loss in competition against the Fusen-ryu style (groundwork specialists). That meant that Maeda too concentrated on groundwork, which would have influenced what he taught Carlos.

Carlos' younger brother, Helio - as mentioned above - was a frail child, meaning that he did not take part in classes at first, simply watching instead. At the time, the system was all private lessons, and one day Carlos was a little late, so the student asked Helio if he wanted to 'play'. Once Carlos arrived and apologised, the student told him that from then on, he wished to learn from Helio instead.

As Helio was much smaller and weaker than his older brother, he couldn't perform the techniques in quite the same way. So, he modified them, preferring leverage instead of strength. Those techniques were further changed after the Gracie Challenge was issued: first Carlos took on various opponents from a number of styles, after which he gradually delegated to Helio (Carlos moved to administrating the academy and developing his nutritional theories, which would eventually lead to the famed 'Gracie Diet'). Techniques were pressure tested in this competition, meaning that anything which didn't work in the challenge matches was either thrown out or modified until it did.

Since then, BJJ has continued to develop, due to involvement in 'vale tudo' ('anything goes', which was the term concocted for the challenge matches), as well as figures like Rolls Gracie, who cross-trained in numerous styles (such as sambo and wrestling). Judo, on the other hand, focused more on throws due to changes in competitive rules, meaning that over time the styles diverged (though its worth noting that the division between stand up, or tachiwaza, and groundwork varies from school to school. There are plenty of judo clubs with excellent groundwork, and others which prefer to work more heavily on throws). Japanese jiu-jitsu was even more varied, as that did not have the same competitive influence to modify the style, though I'd assume it depends on the particular substyle.

If people are looking for further reading on this, I can recommend The Gracie Way and the introductions to Mastering Jujitsu and Brazilian Jiu-Jitsu: Theory and Technique. There's also some discussion in No Holds Barred, and if you can read Portuguese, several books from Brazil.

Once I've got enough reading under my belt, I'll be writing something up on my blog. I love history, as you can probably tell, so enjoy doing that kind of thing.

Oh, and there is some stand-up in BJJ, but like judo, it depends where you go. For example, where I train, class almost always starts with a few throws, or in no-gi, double and single legs.