Star Wars: Clone Wars (2003 TV Series)
This was a limited series of "micro episodes". Each was a short (or "micro") story featuring one or two characters and their actions between Star Wars Episode 2: Attack of the Clones and Star Wars Episode 3: Revenge of the Sith. It primarily dealt with the Jedi, Padme and the droids. The first season featured no spoken dialog. The stories were not meant to be fully realized arcs, just snippets into the universe created to get people excited about the then-upcoming movie (Episode 3).
Star Wars: The Clone Wars (2008 Film)
When screening early footage of the 2008 TV series, the studio heads were so impressed that the decision was made to turn the first few episodes into a theatrical film and release it. It immediately precedes the series and is 100% in continuity with it.
Star Wars: The Clone Wars (2008 TV Series)
This was a long running series featuring many characters and their actions between Star Wars Episode 2: Attack of the Clones and Episode 3: Revenge of the Sith. These are more traditional full-length episodes. In addition to the Jedi, Padme, and the droids, it featured many of the Clone Troops and dealt heavily with the Sith. The characters and stories are fully realized. While some of the scenes and timeframes overlap with the original series of a similar name, the stories are independent. There is no required additional viewing or expectation of knowledge, but it certainly doesn't hurt.
Also, there's a difference in the canonicity. Under the new Disney canon rules, only the 2008 items are part of the New Canon, whereas 2003 TV series is not (it's unspecified yet if it's Legends, but probably is)