Whether the money counts as 'earnings' or not is probably determined by how you made it, rather than by where it is.
For example, if you sell stuff on eBay that you originally bought for your own use, but no longer want, HMRC won't regard the money as taxable income (but it will still be counted as 'savings').
However if you buy stuff specifically to resell on eBay (e.g. from a wholesaler, from charity shops or from local auction houses) then HMRC will regard your profit as taxable income, which must be declared as such. It then becomes 'savings' if you don't spend it.
Either way, HMRC (and the DWP) would regard the money in exactly the same way irrespective of whether it was in your PayPal account or transferred to your bank account.