Bulbapedia doesn’t discern any difference, just says it was reprinted in 99
bulbapedia.bulbagarden.net/wiki/Mew_(WHF_Special_Sheet_promo)
They have the same set symbol, same rarity, neither have numbers, they have the same 1996 copyright date, and they look to have completely identical faces.
The reprint is glossy
I was wrong, they are both glossy
You can only tell them apart when you have the Unpeeled Sheet. Once peeled they become indistinguishable.
*Edit* This information is also valid with regards to the Mewtwo, not just Mew.
Well… one reply says they’re different and one says they’re the same 
They’re the same, and both are glossy. Some old PSA serials say WHF, but now PSA grades them all as the CD promo
They are indistinguishable. PSA labels both cards as CD promo. They used to hand out separate labels for WHF cards if you asked for it and had evidence to back up your request (usually pictures of peeling the card from the vending sheet). They stopped that practice a while ago. Now if you want to prove to potential buyers that your Mew is a WHF variant, it essentially still has to be on the vending sheet UNLESS you have one of the older graded cards with the WHF label. I’ve only seen one of those on ebay as a PSA 10 since May.
In addition, there’s also no PSA population entry for WHF Mew. I do wonder if they combined the prior WHF count with the CD count since, again, it’s one label now.
Thank you sir 
They are the same unfortunately. You’ll notice that the cheaper promo cards tend to have multiple releases, such as the toyota arcanine and this mew card or the mewtwo mentioned above. Cards like toyota pikachu on the other hand come with a nice premium for having the single release and no re-release.
Same card.