Name that movie

I remember long ago, I watched a movie, or something, but not sure what it was called.

I don't have much detail of it, except, one day, loads of fog covered a town or so, and lots of people were trapped in a super market I think. Some tried getting out, but ended up dying. Later in the movie, a few people tried going out through the back, but some weird plant thing started killing them? So the other's had to survive in the super market, until some people managed to get into a car, drive away, only to get killed by a huge beast?

It sounds messed up, but that's what I can remember :(