Are all the eggs that the woman in Lavaridge gives you the same?

Question

I hatched one of her eggs before, and it was a Wynaut. I'm assuming they are all baby Pokémon.

Answer 1

Yes.

Wynaut is a baby Pokémon that the old lady gives you. He is unobtainable in the wild and is referred to as a Gift Pokémon.

You can then receive a Togepi egg from her after beating Groudon / Kyogre.

Hope I helped!

Source: Serebii

Answer 2

Yes, she gives you baby Pokemon...
BUT
she gives you TWO eggs. One Wynaut and a Togepi.

Source: http://serebii.net/omegarubyalphasapphire/gift.shtml

Answer 3

Yes
Actually, she only gives you one Pokemon egg, which is Wynaut
Source