Question

Is there any difference between pressing B and using an Everstone?

Answer 1

Not really, exept that you'll have to press B every time your Pokemon level's up, and when your Pokemon is holding an Everstone, you won't have to worry about your Pokemon evolving.

Answer 2

No, Here are their functions:

Everstone- Go Here:http://pokemondb.net/pokebase/60781/the-everstone-factor
Look at my answer.

When your Pokemon is evolving by Friendship, or Level you may press the B button to stop the evolution process.
The only time you CAN'T press B to stop the evolution process is when you use a Stone.
Stones: Oval Stone, Dusk Stone, ThunderStone, FireStone, WaterStone, Leaf Stone, Dawn Stone, Shiny Stone