OK.. this has to be basic.. but I don't know the answer, so I'll ask.

On door latches there are 2 parts that extend out from the door (which
go into the strike plate). Both can be presssed towards the door.
One is larger in diameter and is the part that latches inside the
strike plate when the door is closed. But there is another, smaller
diameter part that rides right along side the larger one. What is
that for? If you push hard enough, that one can also latch inside the
strike plate. Is it suppose to?

I have an exterior door that does not fit well and leaks air. I think
it needs to be rehung, but if I press hard enough to get that second
bar to latch, it's better.