The meaning is often clear from the context.
-- If a power supply is labelled as having "DC output", then that's a dead steady voltage (nominally).
-- If a power supply is labelled as having "AC output", then that's going to be a square wave or sine wave, centered on zero.
-- The 5Vpp sine wave you describe, superimposed on 3V DC, i.e. ranging from 1V to 6V, would be a bizarre power supply that would be considered faulty regardless of whether it was labelled "AC" or "DC".
So in general, your question "What is my signal ranging from 1V to 6V? AC or DC?" is a fool's errand; a
false dichotomy that no professional engineer is troubled by. See how the terms AC and DC are used in reality, without obsessing over trying to find a precise definition that cleanly slices every possible waveform into one camp or the other.
It's much more useful to think about considering the DC and AC
components of any given signal. The DC component is just the average voltage over time. Subtract that away, and you're left with the AC component. When your multimeter is set to read Volts DC, it (nominally) is telling you the voltage of the DC component, the average voltage. When your multimeter is set to read Volts AC, it (nominally*) gives you the RMS voltage of the AC component of the signal. This ties in with what Benta is saying, if you superimpose (add) the AC and DC components, you get your original signal back.
So I reiterate, your signal ranging from 1V to 6V is
neither AC (as typically defined as mean = 0)
nor DC (as typically defined as perfectly steady; variance = 0). It's a combination of both AC and DC.
*
So many ways this can go wrong in reality in the case of multimeters reading Volts AC, but that's a topic for another day.
Waveforms can simply then be defined as periodic or nonperiodic or as some might prefer repetitive or nonrepetitive.
Tautech, you used this definition to confuse yourself, because it's utterly unrelated to AC vs DC. Sine waves and DC are both periodic, i.e., f(x) = f(x+p) for some period p. But sine waves are clearly AC and DC is clearly DC.