There is a difference between alternate universes and parallel universes, but they are closely linked.
When Rick refers to
Infinite time lines, infinite possibilities. Including a time line where Jerry's a movie star.
this summarizes a theory based on quantum physics wherein whenever a decision is made, the universe is split into two where each different decision is made in either universe (it's much more complicated than that, but that's the gist).
This means that there are infinite universes where different choices have been made leading to different outcomes, and further choices, and further different dimensions, and so on and so forth until there are infinite realities.
This image demonstrates how the different decision will split into alternate dimensions, each has their own timeline where different events have happened in their own past, and thus each has a different reality where they will understand the sequence of events that has happened differently.
So whilst all of the words being used interchangeably refer to pretty much the same thing, timeline refers to the sequence of events that has created that specific universe, and dimension is the universe in which that reality exists.
Note that the words can be used interchangeably because time travels in one direction, and each alternate universe appears to have the same amount of time that has passed (Rick and Morty are always the same age, Tiny Rick notwithstanding).
This happens in S02E01 when Rick uses the time crystal to stop time. It is the same idea as alternate realities, but because Rick, Morty and Summer are out of sync with the rest of the universe's time it causes their own reality to rupture and split off from the rest.
When one of them is indecisive about something, usually two equal and different universes would be created, but because their own personal timeline is so much further forward than the one they are living in they get their own little universe that is massively unstable because it is trying to exist on its own.
So they cannot use the portal gun to travel from the parallel universes because they are around 6 months ahead of any other reality, and they cant travel between each parallel universe because they are so unstable.
As for the portal gun, it can travel both to alternate dimensions and different places in the same universe.