Encyclopædia Britannica says (1a):
Vodka originated in Russia during the 14th century, and the name is a diminutive of the Russian voda (“water”).
At first, Wikipedia sticks to the same nonsense (1b):
The name “vodka” is a diminutive form of the Slavic word voda (water), interpreted as little water.
However, in the same Wikipedia article, an alternative explanation is given (2):
As alcohol had long been used as a basis for medicines, this implies that the term vodka could be a noun derived from the verb vodit’, razvodit’ (водить, разводить), “to dilute with water”.
At least, Викисловарь is less categorical. According to one hypothesis, водка is derived from Polish word wódka, which, in turn, may be a truncated calque of the Latin aqua vitae.
True, one — but not the only — function of Russian suffix -к- is to form diminutives, usually from second-declension nouns. Also, there are other suffixes which are used to this effect. Diminutive of вода (water) is водичка. Diminutive of водка is водочка. There are plenty of second-declension nouns which end with -ка but are not diminutives:
||речка, реченька, речушка
||ручка, рученька, ручонка
Note that the words река and рука don’t have suffixes: in both cases, к is part of a root.
Let’s come back to the hypothesis (2), which relates водка to the verbs водить (to lead, to drive, to move) and разводить (to dilute). It is not as ridiculous as one can think. However, водить, разводить, проводить and so on have nothing to do with water. Have a look at the table:
|водить / вести
||to lead, to drive
|наводить / навести
||to aim, to lead to, to guide
||(lens) focusing; (gun) laying
|проводить / провести
||to conduct, to guide
|разводить / развести
||to separate, to take apart, to dilute
||(saw) setting; drawing (of a bridge)
|сводить / свести
||to bring together
As you can see, the meaning of all the nouns has something to do with “to lead”, “to move”, “to drive”, while the corresponding verbal nouns (apart from водка) mean something that is either a process or a result of that process. Now it would be neat to show that водка is also a result of some driving/moving process. Distillation perhaps?