RMS and Dynamic have nothing to do with how it is being powered. RMS is the amount of power it can put out continually under a certain threshold limit of distortion.
Dynamic power is kind of like Peak power that it can put out for brief loud passages or things like bass notes or the temporarily loud peak dynamics of a band or singer. It's kind of like running a sprint vs. running a marathon... amps can put out more peak dynamic power for musical peaks than they can sustained RMS power.
RMS and Peak is also how power from a signal is measured... RMS is a more conservative measurement, peak and peak-to-peak are measured using more of the waveform.
Like "Music Power" and "Peak Power" are both kind of misleading terms used by some equipment manufacturers or retailers to boost an amplifier's wattage ratings as much as possible to make the amplifier seem more powerful than it really is. Using the RMS power to compare between amplifiers is really the only way to compare power on an apples-to-apples basis.