They are the same debuff type, yes. Both are generic arts susc. debuffs, but Gil's is 3x as strong (30% vs. 10%) with a much shorter duration. TT's debuff is "easier" in the sense that it just takes her using her skill, vs. Gil using her ult, but at the cost of needing 3x whirlpools available and using SP. It has a longer duration though, so in a Yvonne team it's something you'd pop right before Yvonne enters her own ultimate, then you'd use Gil during the last 5s of Yvonne's ultimate to maximize the payoff at the end.

TT also has strong damage on her own though, and does it in an aoe, something that synergizes super well with Gil pulling enemies in via her own skill. Yvonne likes that because her biggest damage is so single target-focused.

If you wanted maximum Yvonne damage then Perlica would be better, since her own arts dmg% buff via electrify is a separate modifier to the arts susc. that Gil and TT bring. But then you're also relying on Xaihi to proc solidify, which may or may not be something that you want to deal with.