"Pursue" and "follow" are sufficiently synonymous that trying to differentiate them becomes a game of semantics. Whatever word you like, he got out of his car and went after Martin.
I disagree, especially in the context they are being used in this case. Look them up in the dictionary:
Pursue:
1. - to follow in order to overtake, capture, kill, etc.; chase.
Follow:
1. - to come after in sequence, order of time, etc.
Pursue implies an intent to capture: I pursued that woman's love; I followed that woman's love. They are not interchangeable.
Also, "went after" sounds like an intent to angrily pursue, or even engage with violence: "Bill said something rude about Jim's mother, so Jim went after Bill".
1. - Prior to GZ getting out of his car, what was he doing? -- He was observing the movements/actions of this unknown, "suspicious" individual and reporting them to the appropriate authorities.
2. - Once this unknown, suspicious person fled (which I think made him appear even more worthy of suspicion, and apparently GZ and the dispatcher did as well) behind houses, was GZ able to continue his observations in the same manner he was previously? -- No.
3. - What did GZ need to do in order to reacquire these observations? -- He needed to alter his vantage point, which required him to go to an area that his truck was not suited for, or capable of reaching. In other words, he had to get out of his vehicle to get there.
Why must his intentions have automatically transformed into a "pursuit", with intent to overtake, capture, or even catch up to (and confront), the instant he got out of his car?
I already discussed earlier how, had GZ been intent on a confrontation, he had a perfect opportunity to do so when TM was just outside of his vehicle. It appears that TM may have even tried to say something to GZ at that time, but it seems pretty clear that GZ did not want a personal interaction with this person.
Listen to this; it's a previously recorded call to the NEN about another suspicious person in the neighborhood. Listen to GZ specifically saying "I don't want to approach him, personally".
http://www.youtube.com/watch?v=NFwh5jcKgn4&t=2m13s