hi, I used to be a chemistry student before switching to biology where i'm now doing biochemistry / molecular biology.
Basically, to me molecular biology is all about DNA, gene expression and genetic engineering. You need a simple understanding of the chemistry involved but it's not really very similar to chemistry. You don't really need to know about mechanism of chemical reactions and such.
Biochemistry, as the name would suggest, is a lot more similar to chemistry.
Perhaps you could say that biochemistry and molecular biology are as much a subset of chemistry as chemistry is a subset of physics.