SMN Summons

I was wondering..
After you get Summoner, you get Ifrit-Egi. Then next is Titan-Egi and last Garuda-Egi.

Does the order mean anything (the power of each)? Like Garuda will do more damage than Ifrit (because ifrit was obtained at lv35 and garuda only at 45)?

I know each has a role, as Ifrit is 'Attacker', Garuda 'Caster' and Titan 'Tanker' as well each of them have the same level as the character itself, but caster type seems the best since has damage and stay away from AoEs (Ifrit is meele, gets hit by aoe easily if I don't stress myself ordering him to come back and go again).

What you guys think?

They're just learned in that order because you have to beat them in the storyline to unlock them. In the storyline, Titan is ~34 and Garuda is ~44.

As far as I know, Ifrit does the most damage but is not always the best pick depending on the boss, as you may have guessed. I know Garuda-egi is the best for the Garuda battle because you have to move around a ton in the fight and Garuda-egi can extend the duration of DoT spells and attack from a distance.

from what I've experienced, Ifrit does some heavy damage and has a melee aoe skill. Many people complain about it's "bad pathing" though. Tanking wise, it's in between Titan and Garuda ( with garuda being the worst to take damage ) . It depends on the situation. Usually though as a DPS, most would consider garuda to be the most effective. I found titan handy when our tankers in dungeon runs were horrible and having an extra tanker to take some damage helped.
but to answer your question more directly . No order does not make a difference.