One of the difficult concepts to understand when dealing with time travel in a Star Trek based universe are the lines that separate different ideas - ideas that were never really explained as more than a basic idea of logic behind what something might be. Beyond Star Trek the Next Generation the science behind concepts also declines greatly making things more difficult.
Time Travel, as a concept, is very similar to the idea of Phasing when explained, but they are portrayed entirely differently in canon. The difference is never explained, of course, because there was no need to for the story lines in the shows. After discussing the ideas about how time travel works in the story line it can become an issue to conceptually difficult understand the difference.
Phasing in Canon Trek
The concept of Phasing is described as being out-of-phase with normal time and in one particular 2 part episode pair (Times Arrow Part 1 and 2 of Star Trek the Next Generation) it is described using the term synchronic-distortion which is further pinned down as being placed out of sync with normal time. So if two people are sitting in a room and person A becomes out of phase and person B does not, then the idea is that person A has phase-shifted either backwards or forward in the current stream of time such that they aren't ever able to catch up or be caught up with. Conceptually this sounds alright except for the fact that in canon being out of phase is shown to have the ability to show an alternate world of sorts that exists on top of this world but cannot be seen (because our eyes never catch up with them).
Similarities to Time Travel
To move into another time person A would have to move out of sync with normal time. Since this isn't just a Star Trek based universe we barrow ideas and concepts from other fiction to help describe the nitty-gritty details. In Back to the Future, Doc Brown described his time machine as going forward in time by one minute by jumping over that minute to land 1 minute in the future. Given this idea the time machine is caught up with. It jumps over the minute and is then caught up with. Conceptually this is much different than being out of phase where you are never caught up with.
Of course in the many descriptions of time travel there are other concepts. There is also the concept of time travel occurring because someone just accelerates or decelerates the speed by which they go through time. This idea is exemplified in The Time Machine by H. G. Wells where his contraption going through time actually does allow him to see time moving outside of his machine. It is simply speeding faster than anything else so no one else can see it.
In Our Writing
n the game Time Travel happens in two ways... There is the concept of the Time Displacement Equipment which I would personally define as being the "Doc Brown" method where a vessel jumps from one point in time to another instantly, skipping over time and space. Differing from that there is the Dimensional Fold Drive which is more of a "Time Machine" method where a vessel goes out of phase with normal time and then accelerates or decelerates the normal passage of time. This is also shared as a concept with the slingshot method used in Star Trek IV, time travel is portrayed as not being instant but a stream of sayings, thoughts, and images which seems to indicate that the crew doesn't just jump instantly but progresses (although extraordinarily quickly) through the timeline to arrive at their destination.
How is this different from Phasing? Becoming asynchronous to normal time sets up the idea that we all live in only a small segment of space-time, our area of space-time being unique and various other areas of out own space-time are invisible to us or barely visible to us. In several different episodes of Star Trek the Next Generation it shows that being out of phase allows one to become invisible, pass through normal matter, perceive but not participate in the normal world, etc.. It isn't inconceivable that if we all find out universe as a starting point that becoming out of sync could allow us to see other streams of time that exist all parallel to us. In fact going out of phase with normal time reveals other worlds with other properties. Then only going slightly out of phase may put a person slightly in-phase with another world allowing a person to perhaps perceive both.
Phasing then becomes different time Time Travel in that Time Travel a person goes somewhere in our own steam of time and existence where as someone going out of Phase shifts out of our own universe/reality into another.