1. Without reskinning - your character is mechanically an elf. In game, he looks like an elf and calls himself an elf.
2. With reskinning - your character is mechanically an elf. In game, he looks like an eladrin and calls himself an eladrin.
Is there any substantive difference between the two?
Yes. Massively. He's not an Eladrin mechanically.
You are playing an elf Cleric and saying it's an Eladrin, not for any roleplaying reasons, but because they are inarguably *better Clerics* than Eladrin mechanically. Eladrin are terrible clerics, and you know this, so in order to get your powergame on, you decide not to use the race you're supposedly using, and use an entirely different race instead.
Again, back to a non-two-kinds-of-elf-like-objects example: 'Drow make lousy shielding Swordmages, let's play a Githyanki but say I'm a drow!'. You're powergaming there. You're taking something else instead of something that exists, because that something else is simply better mechanically.
Basically, you're taking what you want from item A, the roleplaying benefits, whatever they may be to you, of being an Eladrin. But you don't want the mechanical weaknesses of being an Eladrin Cleric. And then you take what you want from item B, the mechanical benefits of being an Elf cleric - +2 WIS, the re-roll ability, increased speed to counter the speed penalty if you're using heavier armor, Seldarine Dedicate is a nice PP that you already have the proficiency you need for, there's a feat for elf clerics that lets an ally within 5 squares spend a healing surge when you hit with your re-roll, etc.
Mechanically, there is no benefit to taking an Eladrin for Cleric, and some major downsides. So you don't take Eladrin, you take elf, but then you say you're an Eladrin. Rather than actually playing the actual race, you use another race entirely for solely mechanical benefit. That's what's powergaming about it. That's the difference.
The option exists. You don't have to reskin or create anything for it. If someone wants to be, say, half-eladrin; the game doesn't have that. You have to create it or houserule it. You might refluff an existing race. You might houserule an existing race. You might just sit down and make a race from scratch because you feel it's something the game should have. But you're creating something that isn't there. There's no half-eladrin. Half-elf doesn't even take the possibility into account in the writeup. You have to make something up for it.
With playing an Elf but saying it's an Eladrin... There are already Eladrin in the game. They're called Eladrin, they come just before Elf in the PHB, you should check them out. If you want to play an Eladrin, play an Eladrin. Don't pick and choose which race's mechanics you want to have for maximum mechanical benefit. That's where 'powergaming' comes in.