AA / AAA (same thing) similarity
At least of the angles of the triangles are congruent. It can be considered as AAA similarity because if two angles are congruent, the last angle is automatically congruent.
SSS similarity
The proportions of the corresponding sides of the triangles are congruent. It has to be all three sides.
SAS similarity
The proportions of two corresponding sides of the triangles are congruent, and the angle between the two sides are congruent.
SSA similarity (uncommon case)
ONLY FOR RIGHT TRIANGLES