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Arguably, I could have done better explaining this, and I probably will revise earlier chapters to more explicitly state this.

All Meta are gravity casters. This is why they have anti-gravity elevators and bridges with both the top and bottom having gravitational pulls, to allow walking on both sides. The time traveling part, though I haven't discussed it much yet in this story, is a power unique to infinity casters.

Now, infinity casters are a special class of caster, and one of the main point of this story is to explore a different type of infinity caster more thoroughly when compared to my main series. The pocketwatch they carry is called a Piece of Infinity, and is only held by an infinity caster. Interestingly enough, it isn't actually necessary for them to be holding it to use their power, but through forces not yet specified in any of my stories, the piece will always find their way back to their owner if lost. It's more of a marker of the power rather than a container for the power.

Ghost was an infinity caster, so is infinity casting just a term for the second casting ability - second ability in general?

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Yeah, kinda... it's almost a separate kind of casting entirely. It's linked to casting type, and is meant to be used in tandem with the standard type of casting. All the secrets behind infinity casting are a large focus for the remaining books I have planned.

Meta is a kind of special case, even among infinity casters. His piece of infinity actually has some functions that can be used with the infinity power, and is also the only type of infinity caster that can work alongside people with the same power at the same time, given the time manipulation aspect.