There are 12 standard Medigap policies to choose from, with the eye-popping names of A through L. Medigap A is the most basic "core" policy. As you move through the alphabet, the plans add more coverage. For example, Medigap E will offer something that is not included in Medigap D, but will lack a coverage provided in Medicare F.
There is no difference in plans offered by different insurers; plan details are all set by the government. (Important caveat: If you live in Massachusetts, Minnesota or Wisconsin, check with your state insurance company or a private insurer who operates in your state. Medigap policies in these states offer coverage different than the plans followed by the 47 other states.)
If you and your spouse want Medigap coverage, you'll need to buy separate policies; spouses aren't covered together.