Well, in a nutshell, if it is something *you* do, it is probably stalking whereas if it is something *I* do, it's surveillance.
Basically, and no doubt this is not something my colleagues would necessarily agree with, the difference is in intent. I am legally entitled to be your proxy stalker as my licence allows me to obtain information, not in the public record, about a person's activities and movements; in this case through direct and covert observation.
If I am reported by a nosy neighbour and the police attend, I can flash my licence and state that I have a lawful reason for sitting in my car with night vision gear for the past 8 hours (or whatever).
If you are reported by a nosy neighbour, however, don't expect the same outcome. That is why you should always hire a professional. We provide plausible deniability.
There are also a number of quite practical reasons why you shouldn't do your own surveillance, particularly if the target knows you. Firstly is that you are more likely to be burned (ie spotted) since the target is able to identify you from a number of visual cues, even if only partially seen. More on this later.
Ultimately, what you do with that information is none of my concern - although there is supposedly an ethical or moral consideration here but I am not my brother's keeper. If a couple weeks later you make the news having been caught with her body in your freezer and her spleen in the frying pan, well, how was I to know?