Yup, they're the same thing. I guess maybe technically "screen printing" is just the printing part while "silk screening" is everything - but people use them synonymously. Here's a video that's pretty helpful: http://www.silkscreeningsupplies.com/site/799934/page/543290
They make it seem like you need to buy all this stuff, but really you can get away with a few basic things. You'll need emulsion, ink (don't use oil-based ink unless you don't the fumes/hassle of cleaning it up w/ turpentine), mesh, a frame, a sink/bathtub (with a decent amount of pressure), a squeegee, and if you want to be precise, some special hinges with clamps for printing. There are a million zines that tell you how to do this diy and a few books, plus you can ask us if you've got specific questions.

If you're going to print fairly-detailed things with thin lines, you should probably get the hinges and mesh with a higher count (thinner holes). Also, if when you print it it's coming out patchy, thin the ink with a little water. No one ever mentions that, but some ink doesn't fit thru the holes of the mesh properly if you're using fine mesh.

Hope that's helpful! You can also find lots of detailed information if you just type "silk screen tutorial" into google. It's a little expensive getting started, but if you throw in a couple choking victim patch designs you can make all your money back.