Checking the online etymological [dictionary] (http://www.etymonline.com/index.php?allowed_in_frame=0&search=Drink+%28n%29+)...

The noun meaning "beverage, alcoholic beverage" was in late Old English. The noun, AS. drinc, would normally have given southern drinch (cf. drench), but has been influenced by the verb.<

So we're looking at the tenth century or so, given the reference to late Old English. Essentially the noun drinc would have, in Old English been different from the verb drincan. In modern English, however the verb and noun have become indistinguishable.

As you can see from the above etymological explanation, even in Old English it could mean any beverage or specifically an alcoholic one.

Edit: I realize I didn't give any information about the two specific phrases but I hope addressing part of the underlying question meets the standards of this subreddit