The Samson's aren't exactly what's thought of as an active studio monitor. The Samson's only have a single stereo amp that's in one of the speakers then you run a speaker cable to the other speaker (which is completely passive). The Samson's are more like regular passive speakers where one speaker happens to have an amp inside.
I'm not saying that's bad. AudioEngine does things the same way. It's more cost effective and convenient to do it that way than have separate mono amps (or in some cases multiple mono amps, one for each driver) in each speaker. One advantage to that setup is that you can have a single volume control built in that controls both speakers. But what you've got with the Samson is more similar to an amp and passive speaker combo than a true active studio monitor.
A true active studio monitor will have mono amps in each speaker with one amp per driver. Rather than having a passive crossover they'll have an active crossover
. You'll need an external volume control of some sort to manage the volume (a mixer, pre-amp, monitor control unit, passive volume control, etc.). So generally less convenient to set up for a desktop setup and require extra equipment to manage the volume.
I haven't heard the Samson so can't comment on them. Based on their size though I don't think the "loud" part is going to happen. Getting them loud would likely cause the sound to become compressed (losing dynamics as they get louder). One feature of active studio monitors is that they generally can get loud without suffering compression.
If you can live with an amp taking up space you can go for a vintage stereo amp and used passive bookshelf speakers while staying in the low budget while getting potentially better sound.