There is much disagreement as to whether the word translated 'carpenter' in:
Matthew 13:55 Is not this the carpenter's son? is not his mother called Mary? and his brethren, James, and Joses, and Simon, and Judas?
and,
Mark 6:3 Is not this the carpenter, the son of Mary, the brother of James, and Joses, and of Juda, and Simon? and are not his sisters here with us? And they were offended at him.
is properly translated or not. In my Interlinear copy that word is actuall in dout as to whether it is:
5045 [e]
tektonos
τέκτονος ?
carpenter
N-GMS
or not, as you can see it is marked with a question mark.
In ancient days they were mostly known as builders, and were not as specialized as they are today. The word tektonos actually refers more to an artisan in wood more than what we consider Carpentry today. That is to say that that particular word is more descriptive of someone who carved wood rather than a builder. Builders were skilled in more than wood as stone was actually more common in buildings of that era. There is a common belief that the word originally used was:
τέκτων tektōn
Thayer Definition:
1) a worker in wood, a carpenter, joiner, builder
1a) a ship’s carpenter or builder
2) any craftsman, or workman
2a) the art of poetry, maker of songs
3) a planner, contriver, plotter
3a) an author
Part of Speech: noun masculine.
If the original word was tekton rather than tektonos, it would explain Joseph's skill in both wood and stone. Many of the old manuscripts are not in very good shape due to the materials written on and the inks used, which are much less permanent than those of more modern times.
As for the term Rabbi it's connotations are much the same as our use of the word 'Pastor' today;
ῥαββί rhabbi
Thayer Definition:
1) my great one, my honourable sir
2) Rabbi, a title used by the Jews to address their teachers (and also honour them when not addressing them)
Part of Speech: noun masculine.
In referring to Jesus it appears that is in reference to his teaching the meaning of the Scriptures:
John 1:38 Then Jesus turned, and saw them following, and saith unto them, What seek ye? They said unto him, Rabbi, (which is to say, being interpreted, Master,) where dwellest thou?
and:
John 3:1 and 2 There was a man of the Pharisees, named Nicodemus, a ruler of the Jews: 2 The same came to Jesus by night, and said unto him, Rabbi, we know that thou art a teacher come from God: for no man can do these miracles that thou doest, except God be with him.
All Scripture is quoted from the King James translation.
Hope this helps.