zu trinken, zum Trinken

[bach]

"zu trinken", infinitive of the verb "trinken", so "to drink". Ok, straight-forward English analogue.

"zum Trinken"? Abbreviation of "zu dem Trinken.", yes?

Literally "to the drinking" (not to the drinks, drinks is Getränken). "Drinking" is a gerund, a verb made into a noun (the "the" in front indicates it must be a noun). Yes?

So, "einen Kaffee zum Trinken" is a coffee to "fill the drink slot". The closest English analogue I can think of is, "as to the drink, I will have a coffee". Yes?

And I imagine in conversation, "zu trinken" and "zum Trinken" sound very similar?

[Cifi]

Your question is not so easy to answer, it's more like nuances in many situations.

I'd use "zum Trinken" if it's about the purpose, as in "Dieses Wasser ist nicht zum Trinken, sondern für den Abwasch".

Thinking of "zu essen" vs "zum Essen", the latter could also mean something like "along with the meal", e.g. "Wir trinken abends Wein zum Essen". But that doesn't apply to "zum Trinken", at least I can't think of any sentence that would make sense.

An construction that came to my mind which only works with infinitive:

Jemandem zu essen / zu trinken geben

[Friedrich Rubinstein]

Jemanden zu essen / zu trinken geben

Jemandem* (:

[Cifi]

Yes, certainly. I'll correct my typo.