What is 2D and 3D thrust vectoring?
As previously seen in a comment section, there are two main schools of thought:


The dimensionality indicates the actuation Degree of Freedom (1D has
1 DoF per exhaust vector, 2D has 2).
The dimensionality indicates the aircraft attitudes that can be affected (2 exhaust vectors with 1 DoF each can affect pitch and roll, hence this would be a 2D thrust vectoring, 2 exhausts with 2 DoFs can affect all 3 attitude angles, hence 3D)


Using the definitions of these two approaches, to make a couple of examples, the F22 thrust vectoring is 1D for the first group and 2D for the second, while the Su30 is 2D and 3D respectively.