What is proving triangles congruent by ASA and AAS

So ASA is angle side angle, and that means that if you prove that the side, and the side adjacent to that side and the angle between those two sides are all congruent to another triangle's sides and angle, the triangles are both congruent.

The AAS is angle angle side, or something, so say you have a triangle and you prove that two of its angles are congruent along with a side to another triangle's, then it's AAS. I understand where the confusion might be. I guess it's just a matter of what you state first in your proof?