The short answer is that it's a pretty subtle, nuanced set of differences that mostly involves tempo and rhythm -- reggae is slower and more kicked-back, and ska is a bit punchier. But we can go a bit deeper here, too.
First of all, it should be noted that for the moment, I'm talking about good old-fashioned first-wave ska, from the island of Jamaica, rather than the much later ska revivalists from the UK or the ska-punk-rockers from the US. This first-wave ska first came about in Jamaica in the early 1960s. It was a natural evolution from traditional Jamaican and pan-Caribbean genres, like mento and calypso, combined with the dramatic new influences of North American R&B, jazz, and early rock and roll, which were wildly popular in the islands at the time.
This early ska was fundamentally dance music, and featured fast, upbeat songs in a 4/4 time signature with heavy syncopation (an emphasis on the 2nd and 4th beats of a measure, known as the backbeat), as well as a guitar or piano line hitting the offbeat (the "ands" in the sequence "1 and 2 and 3 and 4 and") -- this offbeat strike is known as the "skank." Bands tended to feature horn sections, and harmony singers were common, though the songs tended to revolve around a lead singer's solos, with a comparable structure to the soul music that was popular in the United States at the time (and which, according to legend, could be heard on the radio from high-powered radio stations out of Miami and New Orleans).
Listen: Essential Traditional Ska CDs
Now, reggae didn't come about until the late 1960s, but it's important to note the oft-forgotten genre that evolved in between ska and reggae: rocksteady. Rocksteady, popular from 1966-ish to 1968-ish, saw bands slowing down the song tempos a bit and amping up the booming back-beated basslines and one-drop drum lines, while really laying the guitar down loudly on the offbeats. Vocal harmony groups became increasingly important, with many songs being sung entirely in three-part (or more) harmony.
From there, reggae evolved. Reggae found the tempo being slowed down even further, and all of those elements that have become really instantly recognizable as fundamental pieces of the Jamaican music sound becoming really prominent: the syncopated bass line and the one-drop drum hit became loud, and that syncopation drove the sound of the band. The skanking guitar also increased in prominence. The horn lines, instead of following the guitar, tended to be featured in designated spots, and lay quiet in between. The melodies were mostly delivered by a single lead singer, with harmony singers providing secondary vocal lines (there were certainly exceptions to this rule). Remember that lots of ska bands later played reggae without a dramatic change in lineup, so these rules were not hard and fast.
Lyrics also changed quite a bit. Ska and rocksteady songs tended to be fun, upbeat dance-friendly numbers, about love and other lighthearted pursuits. Though there are certainly plenty of songs with these themes throughout the reggae canon, reggae artists also wrote songs about politics, poverty, and religion (reggae gained favor at the same time that Bob Marley converted to Rastafarianism and he began the trend of talking about spirituality in lyrics).
So let's get back to the original question. Ska and reggae are extensions of the same branch of the world music tree, as it were. Ska is an earlier iteration. It's lighter (both musically and lyrically), it's made for fast dancing, and the uniquely Jamaican elements that characterize reggae are less heavily emphasized, though they do exist. I suppose it's fair to say that ska is a sort of proto-reggae, but it's important not to dismiss it as being somehow primitive. Ska was a major musical revolution unto itself (and the difference between ska and, say, earlier Jamaican mento music was far more dramatic than the difference between ska and reggae), much in the way that rock-and-roll drastically changed American popular music.
The moral of this story is that we should all be listening to more ska and more reggae, I think.