[Alfonso]

I think tilde is mostly used for acento ortográfico. When learning to place tildes is very common to hear: todas las palabras tienen acento, pero sólo algunas llevan tilde. So, you use these words to contrast two meanings: acento fónico / tónico and acento ortográfico.
I heard of virgulilla with the nuance Rusty says, but I don't think it's widely used since you don't need to call anything an inseparable part of a letter.
Signo diacrítico (literally, two criteria / two meanings) is also used, but I think it's a more technical concept, as it implies a difference in the meaning of the word. So, there are some tildes that are also signos diacríticos and some that are not.