Drink driving would apply to UK, Australia and New Zealand.
As it implies intent, as opposed to actually being drunk.
You can have a couple of standard alcoholic drinks over a given hour and not be clinically "drunk " as such.
So drink driving leaves things a little more open to explanantion, drunk driving should mean that you were drunk behind the wheel of a car. Which is past tense.
Moral to this story is if you were caught drunk driving, then you have to be drunk, to use the phrase.
As opposed to drink driving, meaning anybody who has had a couple of beers and then gets behind the wheel, technically is or has been drink driving, regardless if they were affected by the alcohol or not.
Which is why most 1st world countries out there have an averaged one size fits all driver blood alcohol measurement road law, of a maximum amount of alcohol that can be tolerated, before it impairs a drivers judgement.
0.5 is the Australian set limit. Which roughly equates to 2 stand alcohollic drinks per hour, all night long with an hour break before you decide to get behind the wheel again.