@andrew's great answer aside, I'll describe the differences in characterization. For the most part, Batman is Batman, the only differences are really how serious the medium makes him. And a good part are actually adaptations of existing comics for Batman. I'm going over the notable ones.
First up is Adam West Batman, from the 1960s TV show, Batman: The Movie, and evidently a few 60s and 70s cartoons. This Batman was very kid friendly, upbeat, borderline ridiculous, and defines camp. Dick Tracy-like, this Batman is basically the late Golden-Age, early Silver-Age comics Batman (1955-1965).
Then there is the Tim Burton's Batman, and Batman Returns. While these are in continuity with Schumacher's Batman Forever and Batman & Robin, their style differ greatly. Burton's Batman drops the camp, and goes with very early Golden-Age (40s) Batman. Some aspects of late 70s Copper-Age Batman too, which also dropped the Silver-Age camp. Grim, noir style. A Brooding bat.
Schumacher's Batman, which again, is technically also Burton's Batman (Burton didn't direct, but he stayed to produced it). Back to a campy, technicolor gadget world. Larger than life. A return to the Silver-Age, well, childish silliness. The only Brooding here is teen Angst Robin.
Between the movies, the cartoons had Bruce Timm. Bruce Timm defined Batman for most anyone under 35 today. The DC Animated Universe Batman was a fairly no nonsense take on Batman. Very Bronze-Age (70-85) serious with a heavy mutual give and take on Modern-Age (85 to then present day 95). Similar to Burton's, not yet on the ultra gritty that 90's comics became. A blend of noir and modern story telling. Didn't patronize kids. Harley Quinn, Renee Montoya, Bullock, many characters born in the cartoon got fully adopted in the comics. The DCAU Batman covers almost 2 decades, including the Justice League Batman, in continuity. Batman has a human side, but it's only revealed around family.
Also includes Batman Beyond, which is in continuity, but nearly 60 years into the future. A different Batman, Terry McGinnis, mentored by Bruce Wayne, who's similar but a teen, deadpan sarcastic joker.
Nolan's Batman is pure Modern-Age (95-Then Present Day). Gritty. Serious Business Batman.
Cartoon wise in the 2000s, we have The Batman which tries to recreate the Tim Burton feel, and Batman: The Brave and the Bold which successfully imitates the Adam West Batman Golden/Silver fantastical whimsy. Young Justice features Batman at times, in a broodier version of the Bruce Timm DCAU, but as the series focuses on the new generation, Dick/Robin/Nightwing and Tim/Robin/Red Robin, again in very Bruce Timm manners.
Finally, we get to the new Batman, Ben Affleck. The grittiest, almost grim dark version, based on the true Modern Frank Miller Dark Knight based. An extreme, non-mainstream version of the Modern-Age. If he was Marvel, he would be XTREME. Essentially the Punisher, minus killing. The most A**hole of the Bats. No nonsense. In the movie, he's dealing with 30 years as Batman, a heavy toll has destroyed any sense of humor. He's not the occasionally cheerful Bruce every other version has.
In short, most are the same Batman, but it ebbs back and forth on the level of seriousness, depending on which era of comic Batman they are following. As the modern comic trend is darker, meaner, grittier, this is what you get in film and tv.
Don't even get me started on Flashpoint Batman.