What are the different kinds of "spackle"?
Spackle is a brand name for a wall patching compound.

Joint compound is what is used to smooth over the butt joints and corners of newly installed drywall aka gypsum wallboard in order to achieve a finished surface. 

Setting type joint compound such as Durabond 45 or similar (the number indicates the 'open time' or workable time but it's usually significantly less than the number stated in real life) is a fast setting and tough compound that can be used for either patching or for the first coat of 'mud' when taping drywall joints. 

Be careful when using the pre-mixed 'spackle' type products. The are easy to use and dry or 'set' quickly but they are very soft and more easily dented than the setting type joint compounds.