NOTE: older thread
To simmer implies cooking in a small amount of liquid (more liquid would be "to braise")
I've always thought it was just the opposite, i.e. simmering, which is just under a boil, almost by definition requires a certain amount of liquid. Braising can be done with less liquid, which is often in the form fat. But I don't cook and am just relying on memory from watching someone else cook or on dictionary definitions.
Here, for example, are the relevant entries from the OED (Second Edition, 1989):
1. intransitive Of liquids: To make a subdued murmuring sound under the influence of continued heat; to be at a heat just below boiling-point.
2. transitive To keep in a heated condition just below boiling-point.
To cook à la braise; i.e. to stew in a tightly-closed pan (properly with a charcoal fire above and below), the meat being surrounded with slices of bacon, herbs, etc.
a. transitive To boil slowly in a closed vessel; to cook (meat, fruit, etc.) in a liquid kept at the simmering-point.
b. intransitive Of meat, fruit, etc.: To undergo stewing; to be cooked by slow boiling in a closed vessel.
sauté, verb = sauter, verb
transitive (See quot.)
1869 Gouffé Roy. Cookery Bk. i. 5 To sauter is to fry with little butter over a brisk fire.
BTW, pan-seared was added in 2005 to the definition of the noun pan, but I don't have access to that definition.