You are right, you don't get paid when not working - that isn't really surprising though, is it?
A teacher on a contract gets the salary divided into 12 equal portions, so, for your family budget, it is easier. A teacher doing supply, used to get the full salary, divided by 195, for each day they worked. This was, of course, back in the day, when supply teachers just were bought in directly by schools. Now virtually everyone goes via agencies, you earn less, as the agency takes a cut.
The reason it is 'easier' or less stressful, if that you only do the 'teaching' - that is, be there in front of the class, and then mark / clear up after yourself. You don't have to do the other crap that comes with the job - such as the constant tracking / data etc. Nor do you do staff meetings, parents evenings, nor will you be planning assemblies, trips, residentials, attending meetings with outside agencies etc etc
Disadvantages are you don't get included in any training (well, with some trainings this can be seen as an advantage
, but with a lot, you can soon miss all the changes that happen constantly in teaching. You don't know the dcs' names or their particular difficulties or additional needs. You don't know the schools policies re things like behaviour or even things like if they are allowed to go out to the toilet or not. You don't know the timetable of the day. You don't know where anything is etc.etc (unless you get a regular lot of supply in one school).
Another downside is you don't get to know the dc, and see them progress, and help them to overcome whatever it is they are struggling with.
If you have young dc and need childcare, then you need to be paying for childcare (to be available yourself) but might not get work and therefore not paid. Or, you don't pay for childcare, and then you can't accept the job as you haven't got childcare. It doesn't work at all well for those who need childcare.