You're right; there are different degrees of kosher, as well as different organizations that supervise, some more strict than others. The basic gist is that meat and dairy are never mixed at the same meal. Eggs and fish are neutral (parve), and can be served at any meal. Foods that are completely off-limits are pork, shellfish, fish that do not have scales, and any animal that does not have a cloven hoof. The rear portion of the cow (or that type of livestock) is also off limits.
In a very strict kitchen, you will find rules regarding dairy, and it will require a separate supervision called Kof-K.
There is a special trademark on the packaging that will identify what organization supervised the manufacture of the product--Not only with dairy, but with all foods. Some of the symbols you might find are: "K", "K surrounded by an O", "KP" (meaning kosher parve), Or "KD"(kosher dairy). Then there are marks for Kosher for Passover (which has a whole different set of rules).
Meats that are strictly supervised would be called glatt kosher.
Gelatin is usually not kosher, but there are certian types made from vegetable sources, that are. There is also a very expensive variety made from the inside lining of a cow's stomach--oddly, it's considered dairy, because that's where the milk is produced.
Then there are ways to actually kosher surfaces and utensils in a kitchen , which entails boiling water and salt. A kosher professional kitchen has someone on the premises to oversee the work, and make sure that rules are abided by. This person is called a maschiach.
I have a lot of personal and professional experience with this subject, as you can tell.