So what do you think of time? Is it like a river/stream and we're a leaf floating along, is it static or pulsing or what?
With the advent of special relativity, people realized that space and time were entangled so to say. And the entanglement is different for observers who move relative to each other. Most time travelling ideas that are feasible are based on general and special relativity.
The SI definition of time is based on atomic clocks:
"One second is the time taken by 9 192 631 770 oscillations of the light (of a specified
wavelength) emitted by a cesium-133 atom."
However even more accurate atomic clocks are currently being developed.
Also as we've found there are different types of gravity
I've never heard of this. Please clarify. I'm pretty sure gravitation is universal.
Would we have to define what type of time we're talking about?
Well there is Newtonian time which thought that time is same everywhere in the universe. This of course was wrong after the advent of the discovery of special relativity by Einstein. Time is relativistic. Time is experienced differently for someone in space than someone on Earth and is experienced differently for a stationary person than person travelling at a high velocity.