Generally exploring is classified as simply going where you're not allowed to go in places. There's a fair numbers of "types" if exploration. When you explore an active site it's often considered active infiltration. It's totally exploring and it's one of the most ballsy forms of exploring (depending on the location).
A good example of exploring something that is not abandoned/decaying/ruined is draining and tunnel exploring. It's definitely not sanctioned and depending on where you're going/what you're in you could get into big big trouble for it. Draining is one of my favorite types of exploring, and really if a drain is "abandoned" as it were...it could potentially be super danger and not something you should ever really do (gases in drains that aren't moving/active can be deadly). So active drains are the shit and I love going in those.
Let me clarify, though, that the more trouble you can get in doesn't make it a better explore of more legit or cooler. If you have permission to go into a derelict building...that's still exploring and completely acceptable.
Some of the best explores I've been on were with permission.
"Qualifications" for exploring are up to interpretation and some things are cooler than others, and it's really not a black and white issue. That being said, walking into the "Employees Only" break room of your local Best Buy doesn't really count.