These verbs have pretty much the same meaning.
To pull over - If a vehicle or driver pulls over, it stops by the side of the road.
To park - To leave a vehicle into a place where you are going to leave it for a period of time.
For example.
Let's pull over and have a look at the map.
Can we say
Let's park and have a look at the map.
with the same meaning?
In the senses that you give above, we use pull over more often to indicate a brief pause while travelling: to look at a map, to let others pass in front, in response to a police car's red light, etc. We can also pull over without stopping, while to park implies stopping.
We use park more often to indicate a longer stop at a destination.
We can say Let's park and have a look at the map with the basic meaning of stopping clear, but it would be more common to use pull over in that utterance.
"Pull over" is more of parking away from the road proper in order to do something (like getting snacks, or for police).
Can we pull over, because I want to eat.
The police pulled him over to test him for drunk driving.
"Park" is used generally for leaving one's own vehicle/whatever (stationary) at a place.
He parked his car in his driveway, and now someone broke the car window.
"Pull over" is more specific on the manner of how/why the car gets parked, while "park" doesn't have such implications.
In your case, they pretty much have the same meaning, except with the specific-ness I noted above.
And to specify where you want to stop and look at the map, you ...
... pull over to the curb.
but
... park at the curb.
or
... park by the curb.
(or ... park on the curb.)
"Pull over" generally means to stop at the side of the road, in a place where you normally wouldn't park for an extended period of time (i.e., not in a designated parking space).
On the other hand, you "park" in a variety of places: a parking lot, a driveway, a parking space, etc. You don't usually "pull over" into those places.
