In order to comply with US export regulations, you have to first determine the Export Control Classification Number (ECCN) for any item(s) you wish to export, which will then tell you what export controls that item is subject to. From there, you have to refer to a set of country lists to determine if the country you want to export the item to is subject to those particular export controls. You ALSO have to refer to a list of parties (individuals and companies) to whom exporting certain items is prohibited. If the item you want to export is controlled for the destination entity or country, then you either can't export it at all, or in some cases must obtain a permit to export it. You are also required to ensure that you're not exporting to someone who will subsequently transfer the item to a prohibited country or entity, which is why some sellers don't ship to reshippers. It doesn't matter what the item is or if it is new or used, the same process applies.
eBay doesn't actually do any exporting, it's just an auction house essentially, so export compliance is the seller/shipper's responsibility. Amazon, AFAIK, mostly ships from regional subsidiaries, so if you're in Europe, for instance, you're purchasing from warehouses in the EU, generally, so nothing is getting exported from the US to you by Amazon. If the item originated in the US, then presumably export compliance was handled via the manufacturer or distributor who provided it to Amazon, and is known to be under no export controls that would prohibit its general sale onward from there.
Same thing with other large distributors, presumably they handle all of the export compliance for US-origin items when those items are either transferred internally from a US location to a non-US location, or when the item is acquired from a distributor. If you order from a US supplier directly, then the supplier is obligated to export an item to you only in compliance with applicable controls. I'm not familiar with other countries' export rules, but I imagine that they get handled the same way, IE, at the time of export from the country in question.