Although your son is on overstay, children are not fined or banned, so there isn't an issue with him remaining in Thailand. When he leaves Thailand, you should try to get him proper visa to return. Unless he's likely to remain in Thailand for a long time and go to school here, it's not really an issue if he doesn't have a proper visa.
Children who overstay are stamped as such in their passport. They are just not fined or banned. Having an overstay may cause issues if they want to attend school in Thailand.
Generally speaking a visa is something you buy before you travel, that allows you to enter a country for specific reason. On entry, your passport is stamped with a date that you have to leave by, depending on the visa you bought. An extension is something you buy inside Thailand at an Immigration office - it's a stamp that permits you to stay for a specific period of time and for a specific reason (e.g. Retirement/Marriage to a Thai/Work).