When speaking in my woodshop, I can't quite tell whether people are saying joint or join when referring to the place where two pieces of wood are glued (or nailed) together. I know the practice is known as joinery but in my use of the English language, joint seems more appropriate. Of course, it doesn't help that a jointer is a tool for a completely different thing.
Good question - given that wood working and the language we use to describe it are hundreds of years old, I will assume both words have been used interchangeably here and there.
In my experience, I have heard it as a joint (being the noun describing two or more pieces of wood stuck together). I felt that I should consult a higher authority, so I went to Joseph Moxon's Mechanick Exercises or Doctrine of handy-works (1703), one of the earliest books on woodworking in English. Thanks to google, I could search the text.
Moxon is consistent: join is a verb ("these two Pieces are with Glew commonly join'ed together", p.64) and joint is a noun ("...smear the Glew well upon the Joint of each piece you are to Glew together", p.105). I hope that helps.
You asked about the word for the place where too pieces of wood meet. This is definitely a joint and probably should not be called a join.
However to further add to the fun here, when referencing the machine known as a Jointer, I have always heard the action of using this particular tool described by the verb joint.
"Be sure you check the fence on the jointer table before you joint those boards. I was jointing something at a 2 degree angle earlier today, so it may not be square."
Not sure if this is colloquial or correct english, but I have heard this verb used constantly in several shops I have worked in over the years when referring to the act of using the jointer. I have not ever heard the more general act of creating a joint called jointing to be clear, just the act of using the machine. This would merely be referred to as joining or cutting joinery.
It is worth nothing many people call the machine jointer a joiner which is incorrect and very hard to distinguish from the correct name. :)