IIRC, in the UK, "hunting" is riding to the hounds such as in pursuit of fox. Most of what we Americans call hunting, they call shooting.
Lately, for my purposes, hunting is mostly a legal term encompassing the pursuit and taking of game. What I do most with consideration to the "hunting" label is, depending on open/closed seasons, not much in the way of pursuit, but plenty of year-round observation with the occasional one-shot to harvest (aka kill).
I've been lucky in that the deer like my backyard. They're generally always around and enjoyable to see.