Not to mention, the show is actually filmed with a live audience.
There's a difference between a studio audience and a live audience.
Saturday Night Live has a live audience. The audience who watches the show will see the entire episode live, and all of the actors have to deliver their lines perfectly.
Big Bang Theory has a studio audience, meaning people come in and watch the episode being made essentially. They'll sit through actors rehearsing scenes, and they'll laugh and the best laugh tracks are added to the final product.