Just found the answer to a question and wanted to share.
It seems that Trizma is just a trademark name. But it is exactly the same as Tris. So if you read Trizma-HCl in a protocol, you can just get Tris-HCl.
The chemical formulas match, Sigma says NH2C(CH2OH)3 · HCl for Trizma, Wikipedia says C4H11NO3 for Tris. The structural formula is ident. Both are powders, so you determine the concentration anyways.