Just to add to BP’s comments, I’d add that the electricity meter controls the supply to the heating elements, switching power to them at the start of the offpeak periods and away again at the end. A thermostat controls when they switch off during the period.
However, the heater still needs to have some power during the day, both to run the electronic controls and to run the fan that sucks in cold air, heats it up and blows it out again when you need warming up - the ‘Comfort On’ periods. This power is supplied by the same circuit as everything else you use during the day, but the heater won’t draw more than about 20W even while the fan is running. Only if you activate the Boost function will you be consuming lots of energy at peak prices.
The upshot is that both switches should be on all the time when you need the heater to work.
I’m a bit confused by your first screenshot, because the time periods shown are the ones when the heater will be blowing out heat (the display showing Comfort On). On an ‘Out all day’ scheme, I would expect to see the time periods set to something like half an hour before getting-up time to half an hour before going to work, and then half an hour before you get home to half an hour before bedtime. You should also be able to set a different schedule for, say, weekends, when you might get up later and be at home for at least some of the day. Unless you have an unusual Sunday schedule, I wouldn’t expect you to want to be having the house nice and warm between four and six in the morning. You can set different time periods for each day of the week.
Let us know if this doesn’t make sense.
[Full disclosure: I have heaters with just the same control as the one shown in your screenshot.]