H1B or J1..confusion

H1B or J1..confusion

Dear Fellow at SOPS,
I will be soon joining UM as a postdoctoral fellow, I am pleased to notice
that there is a society for PDA's at UCLA. I have obtained a lot of useful
information on this site and I appreciate your effort to keep it updated.
However, I have not found an answer to one question that I am facing and
there are plenty of mixed answers on this available on different forums. I hope you can help me with this.
My question is that, once I join university as a postdoctoral researcher
(freshly graduated) on H1 visa, and say after working at the university
for one year, if I further want to join a company for which attorney from
the company will have to file new H1B application for me. Will my new
application be counted for a VISA CAP (which is currently 65000 per year).
Because my old H1B visa, which was from the University, naturally it was
not counted for the CAP as universities are exempted from the CAP.
Thankyou for your help.