When I turned my heat on, it failed to heat properly.
I put the settings on( Auto and Heat). It still failed to heat properly.
So then I proceeded and put the settings on (On and Heat)
It then started to heat properly.
But, I know the settings should be (Auto and Heat). But, when I put it on (Auto and Heat)
It stopped heating.

What really are the correct settings to put the heating system on?

Heat and Auto then set desired temperature. Auto/On is for the fan/blower control only. On is ON all the time and Auto is when the fan/blower only runs during the Heat cycle only.