When I worked for an eBay seller ~5 years ago, we sold a lot of product on both eBay and Amazon Marketplace.

Given we often had inventory available in FBA (Fulfillment by Amazon) and not in our own warehouse, we often fulfilled eBay orders via FBA.

I've been out of the business for awhile, I think the rules around this from eBay's end have changed. Regardless, it's common for sellers to use 3PL (third-party warehousing and fulfillment) services, FBA or otherwise.