There are 3 (not 2) products you might be working with. Two of them are Arm & Hammer, so be careful!

Arm & Hammer Baking soda is sodium bicarb. It is generally used in BBB for raising alkalinity, but does raise PH as well.

Arm & Hammer Washing soda is sodium carbonate (I think, I am sure Richard aka Chem_geek will jump in soon). Also know as Soda ash. It raises PH a lot (about twice as much per measure as borax). Not sure what it does to alk.

Borax (20 Mule Team, green box) raises PH, but not alk.

You don't want the Baking Soda, your TA if fine. You can use Borax or washing soda. Most on this site would use Borax.