I happened to look at the specs of another Hantek (DSO5000P).
The description is more detailed, but I understand even less.
For CAT I and II it also says 300Vrms (10x) like mine, but for CAT III it says 150Vrms (1x).
What does that mean? Does anyone understand this?
I'm actually about to release a video on this topic ("Understanding CAT Ratings") but it won't be on YouTube for a few weeks.
In the meantime: there are four CAT ratings, each representing a higher voltage (and higher danger) environment. In addition, within each CAT rating there are rated voltages. (See attached slide). The combination of these determines the maximum transient voltage. Using that voltage and the "test impedance" at the bottom, you can calculate the max working current and max transient current.
So
CAT II, 300V has 2500V peak and (2500/12 ~=) 208 amps peak current
CAT III, 150V has the same peak (2500V) but since the test impedance is 2 ohms (vs. 12 for CATII), the max current is 1250 amps
So it should be clear (although maybe a little counterintuitive) that the CAT III, 150V device is "safer" than the CAT II, 300V device.
(But the CAT III device will also be more expensive, generally speaking)
The general recommendation (assuming you have choices) is to choose the category you will be working on, then a rated voltage within that category.
Normally, electronics (running on DC) is CAT I, household appliances or anything you plug into a wall is CAT II, indoor distribution wiring and things that are wired in (vs. plugged in) are CAT III, and the outdoor power connection from the utility company is CAT IV.
Hope that helps. I'll post a link to the video when it's live on the R&S YouTube channel.