Esper is really just kind of a preferred word. Psychic has too many weird associations so I only use it in a more tongue-in-cheek kind of way. And any time I try to come up with a unique word for Espers, it typically just feels too quirky and unrealistic for the setting when a word like "Esper" is convenient and right there.
That's why I tend to default to it in any settings with people who have some kind of psychokinetic ability. It's just simple, to the point, and sounds good.
All my settings are somewhat connected by thin lore similarities but the time lines for WSC and GS don't align well enough for these to really be in the same universe. I think I was originally considering if they would be but there were just inconsistencies that wouldn't really work out.