At first, this may seem a tough nut to crack.
But it boils down to a few things.
1. Buddhism is an -ism, meaning largely "adherence or following an ideology or philosophical world views", dharma is not bound by such as it is more in the line of "the fundamental truths".
2. Buddhism is something you "follow" or "do" (note the ""), dharma "is" what "is".
If you come this far, tag along a little further, because now it gets interesting.
As a buddhist and not a "wordwrangler" you don't have a difference since what you do is what is.
Meaning, that there is no difference between Buddhism and Dharma.
"What's in a name? That which we call a rose
By any other name would smell as sweet."
- Shakespeare, romeo and juliet
Or as another master would say:
"No! No different! Only different in your mind."