In linguistics, what is it called when the sound of a letter can be continued (like sssss or mmmmm)?

Try looking into Sonorant, Continuant, and Voiced consonants. The term fricative corresponds to the friction involved in producing certain sounds such as S and F; M is a nasal consonant.

M is a: Nasal Stop, usually shortened to nasal, where there is complete occlusion of the oral cavity, and the air passes instead through the nose. The shape and position of the tongue determine the resonant cavity that gives different nasal stops their characteristic sounds. Examples include English /m, n/. Nearly all languages have nasals, the only exceptions being in the area of Puget Sound and a single language on Bougainville Island.

S is a Fricative, sometimes called spirant, where there is continuous frication (turbulent and noisy airflow) at the place of articulation. Examples include English /f, s/ (voiceless), /v, z/ (voiced), etc. Most languages have fricatives, though many have only an /s/. However, the Australian languages are almost completely devoid of fricatives of any kind.

T is aPlosive, or oral stop, where there is complete occlusion (blockage) of both the oral and nasal cavities of the vocal tract, and therefore no air flow. Examples include English /p t k/ (voiceless) and /b d g/ (voiced). If the consonant is voiced, the voicing is the only sound made during occlusion; if it is voiceless, a plosive is completely silent. What we hear as a /p/ or /k/ is the effect that the onset of the occlusion has on the preceding vowel, and well as the release burst and its effect on the following vowel. The shape and position of the tongue (the place of articulation) determine the resonant cavity that gives different plosives their characteristic sounds. All languages have plosives.

An English R would be a Approximant, where there is very little obstruction. Examples include English /w/ and /r/. In some languages, such as Spanish, there are sounds which seem to fall between fricative and approximant.

Hope this answers your question.

Fricative?