Custodial Roth IRA annual limits for 2023

I understand I have until April 15, 2024 to contribute to my kids custodial roth IRA.  I read that the max contribution is $6500 for 2023 and parents can contribute/match up to what the child earned.  

So does that mean if I child earned $6500 annually in earned income for 2023, I can contribute another $6500, for a total for $6500 + $6500 = $13,000 in 2023?  Or does that just mean the MAXIMUM contribution total of child's earned income + parents contribution = $6500?

 

What is not clear to me is if I pay them to say, walk our dogs or clean the house, if that counts as earned income.  Or does it have to be a neighbor paying them to walk their dogs or do chores?  Do parent's paying their own kids in case, to do things count as earned income?