Colloquially, this type of fold is known as a "break". As the name indicates, with this type of fold the paper is folded once.
As the image shows, the paper is "folded in". This results in two parallel breaks. Due to the closed edges that arise from this type of fold, items folded in this way can be stuffed into envelopes with machines.
Colloquially, this type of fold is often referred to as a "cross-break", as the breaks meet one another at 90° angles. Most of the time two breaks are folded, but more folds are possible. Thanks to the closed edges, machine processing is possible.
With this type of fold, the paper is folded alternately forward and backward. The fan fold is comprised of two or more parallel breaks. Fan folding is not suitable for machine enveloping, as it does not result in any closed lengthwise edges.
As the image shows, after being folded the paper looks like it has two wings, just as one sees in a window or altar; hence the name. With this type of fold there are two parallel breaks. This way of folding looks elegant and is often used for invitations and such.