In the MY INFO section you will enter either your SS# or the ITIN ... that is the only place either of those numbers are entered in the TT program.
If you have a Sch C, in the business info section you will have the option to enter the businesses EIN if you have one.
Your TIN is your Social Security number. You only enter the SS number where asked for the SS number and enter the EIN where asked for the EIN. If you are completing a Schedule C for self-employed income and expenses then you can enter either your SS number or the EIN you received from the IRS.