That is linking them. PayPal knows what sites the person used before sending payments. eBay says they allow a user to have 1 PayPal and 2 eBay accounts, but I have never been able to link even two high feedback and highly reputable accounts together without any issues. It's been a problem every single times I've done it, and has resulted in me either:
Losing 1 Account
Losing Both Accounts
Being restricted on Both Accounts to how much I could earn or how many items I could sell or have listed.