Odd problem with `Module` and `Block`

Question

I found some bizarre phenomena in my code. While I'm using Module in my function, the result is incompatible with which I did outside Module, and when I replaced Module with Block it went back to normal. I don't know why.

Edit:

Now the problem becomes this:

Module[{a,b},
a=Sin[x];
b[x_]=a;
b[y]
]

doesn't give Sin[y], while Block gives Sin[y].