Very smart question! There is a lot of confusion on this topic.
The short answer is: there is no difference. We physicists like to say, with a little smugness, that “chemistry is only applied physics”. What we mean is that all chemical reactions could be described as physical processes. Why don’t we do so? Let’s go into the long answer.
Chemistry is about how atoms combine to form molecules. Atoms have a tendency to stick to each other; they do so because they contain electrons and protons, which are electrically charged particles (negative and positive). These particles attract or repel each other, and this makes atoms stick together. You probably already know this kind of forces: there is a very easy experiment where you rub a pen against a wool sweater and then you can use it to attract small pieces of paper. That happens because some electrons have been moved from the wool to the pen, and the pen is now charged. This is a physical process! The same kind of forces are what keeps atoms together in molecules. So why do we need chemistry?
Well, we need it because figuring out HOW atoms stick together just by considering them made of electrons and protons (and neutrons, but those don’t matter much) and calculating what happens is VERY hard. It’s part of what I do, because sometimes it can be useful, and it requires lots of calculations with very big computers. Experience however teaches us that atoms tend to stick together in similar ways: for example, a carbon atom usually sticks to four more atoms – sometimes with less than that, but in that case it will form “double” or “triple” bonds with some of them, so that the total number of bonds is still four. This is not a rule of nature: it is just a consequence of how carbon atoms are made, and is true in most – not all – cases. Chemistry is the knowledge of all these practical rules, all the ways the atoms usually behave (as well as of which are the exceptions to their usual behaviour) when they react together.
So usually we define as “chemical” reactions those specific physical reactions which involve atoms sticking together or separating themselves to form one or more molecules, and that have their own special set of rules, while we define “physical” reactions all those processes that can be explained by physics but don’t quite fit into that description. Physics is behind all of it, really, but if we had to take it into account every time, it would be like needing to re-invent the wheel every time you want to build a new car!