I chatted with anongoodnurse about this (transcript) and turn it into an answer (trimming it somewhat).
First, I asked:
Regarding bed-wetting and enuresis, the way I understand it, enuresis occurs at an age when children usually can control their bladder, around age 4. Looking at the questions tagged bed-wetting, there are some about much younger children, e. g. one is 2 years old. Would tag enuresis make sense in such cases?
I've never seen the term enuresis applied to a situation below the age of five either, and a quick look at the literature (the general literature, like treatment options) shows that attempts to treat don't begin before age 5.
There are several definitions used for enuresis. One of the most popular is the ICCS:The International Children's Continence Society has developed standardized terminology for lower urinary tract function and malfunction in children.
Enuresis (synonymous with intermittent nocturnal incontinence) refers to discrete episodes of urinary incontinence during sleep in children ≥5 years of age. Before then, it's referred to as urinary incontinence, or bed wetting. The ICCS does take note of diurnal enuresis as well.
So we came to the conclusion that both, enuresis and bed-wetting are needed. For younger children, bed-wetting will be used, for older children enuresis.