In your case, the difference between "employed" and "self-employed" as a babysitter is one of who takes responsibility for your tax payments (withholding) reporting.
"Employed" means you are an employee of someone else . That employer pays you, withholds tax (income, Social Security and Medicare), pays a portion (1/2) of your Social Security and Medicare tax for you, pays unemployment insurance premiums for you, probably workman's compensation insurance, and probably some other taxes as well.
"Self-employed" means you work for yourself, and take personal responsibility for all your tax obligations. The people who work for you only give you cash or a check for your work. You have to plan for, budget and pay all your tax obligations. If you aren't able to work or can't find work, your income stops.
The Differences Between Employed vs. Self-Employed
