Ariel,
>is there a difference in the actual form of the letters between the old Tekton and Tekton Pro?
Generally speaking, probably not. Although they are differently named and coded, in most cases when Adobe converted its PostScript library to OpenType, the metrics and glyphs were replicated, and in some cases additional glyphs added and "expert sets" or "alternates" combined. If a job was set originally in Tekton (PostScript Type 1), and converted to Tekton Pro, you
might get some text reflow, so a careful proofing would be suggested.
What is your client's specific concern? If you submit proofs/final art as PDFs with fonts embedded, your client doesn't have to worry about this.
>In the case of Garamond and Garamond Premier Pro...
Which "Garamonds" are you comparing? There are many different cuts of Garamond, and Garamond-like fonts that look similar in design and construction, but are indeed different fonts. For example: ITC Garamond, Adobe Garamond, Garamond No. 1, 2, 3, etc., Garamond Premier Pro, Garamond Premiere Pro Opticals, ITC Garamond Handtooled, Simoncini Garamond, Stempel Garamond, Italian Garamond, Monotype Garamond, Berthold Garamond, Garamont, Old Claude, Augereau, Sabon...and that's just scratching the surface.
Neil