Most alternative and contemporary metal rings are made in a comfort fit style. Comfort fit rings are curved on the inside. It makes them a little easier to take on and off. As the name suggests, it also makes them a little more comfortable to wear.
The curve on the inside of the ring is similar to the side of a barrel. The top and bottom are carved out a little bit, so there is less material on those parts of the ring than there would be on a standard fit ring. This is why comfort rings are just a little bit bigger, and also why they feel better on your hand when you're wearing it every day.
Rings made from gold, silver, platinum, and most other traditional wedding band materials are usually standard fit. The inside of the ring is flat from top to bottom.
The main reason to know about comfort fit is for ring sizing. Most of the time, a standard fit size is also the size you should order for a comfort fit ring. However, the size and width of the ring may make a slight difference.
If you're ordering a thin ring in the 1mm - 4mm range, the comfort fit likely won't make a difference.
For rings that are 5mm - 6mm, your standard fit size will likely be the right size for the comfort fit ring too. However, if you know your quarter ring size (which isn't necessary for most non-precious metal rings), you may want to err on the side of smaller.
For rings 7mm - 9mm, you may want to order a half size down from your regular size.
Ordering a half size smaller than your standard fit size is advisable for rings that are 10mm - 20mm in width.