The short answer to your question is: Yes.
Implants come in different lengths and diameters, with average sizes in the 3 to 6 mm range.
The posts for implants (which we call abutments) also come in different lengths and diameters.
The diameter fits the implant placed, and the length of the post, i.e. abutment, is chosen according to the space available and the type of restoration that will go on top of the implant, for example a crown or a denture.
Good luck, and I hope I have answered your question.
Carlos Boudet, DDS, DICOI