Technically, there is likely to be little difference between the types apart from packaging. The designs used inside MI specific products will not be different in any sort of fundamental way than the PA designs. Specific details such as size, power, voicing etc will differ.
It's still two discussions. I am again addressing the original poster's question about lightweight amps... integrated bass heads that use a variety of technologies to stay small and light... class D amps, SMPS power supplies, and various combinations of power amp and power supply designs along with integrated preamps specifically voiced for a certain tones, etc.
Since integrated bass amps with similar spec's on paper sound VERY different due to a lot of different issues, it's a totally different discussion to me, and both are interesting in their own right.
Whether a 500 watt class D integrated bass amps with an SMPS techically can sound the same as a 500 watt class A/B amp with a toroidal power supply is a moot point to me... all I know is the Markbass F1 sounds TOTALLY different than the AG500, and that's what I'm attempting to address for the OP! While one is class D/SMPS, and the other is class A/B toroidal is interesting to me, it's secondary to the different voicings and tone these amps have.
I do very much enjoy learing about the technical issues involved in these discussions though... so let's all keep at it!