It's hard to teach calculus over the net. I would go over to wolfram and learn the differences...

In general, though, delta simply means change. As far as partial derivatives go, they are used because most functions (or dependent variables) depend on more than one variable. So a partial derivative of a function f with respect to variable x signifies the (infinitesimal) change in f over the (infinitesimal) change in x, while holding all the other variables (y, z, etc..) constant.