Bottling mead and beer are the same animal or at least the same species.
With Still meads, you just don't use priming sugar when you bottle. You also want to hit it with sulfite and sorbate to make sure fermentation doesn't renew. Still meads can be bottled in anything really. Swing tops, crown cap beer bottles, corked wine bottles, etc.
When carbonating meads, It's important to make sure you have the right bottles, or else your just producing high pressure glass grenades. Beer bottles and Champagne wine bottles will be your go to. Regular wine bottles will not hold pressure and will either blow the cork, making a big mess -OR- blow up, maybe hurt someone, and make a bigger mess. Champagne bottles use their fancy corks and cages. When carbonating, you don't want to hit it with stabilizers because you want the yeast to get at the priming sugar.