The customs bill is the VAT bill.
Umm, no? Whenever I have received anything from the US from Digikey, there were
always separate items for VAT and customs. The "customs" part typically includes both the duty and also the handling/papework fees of the company doing the processing for you (aka Fedex/UPS/etc. in this case). I recall having to pay the VAT on the spot to the courrier and then two weeks or so later I got a bill for the customs and fees from the transportation company.
These are definitely separate items, collected by different parts of the government in most places.
VAT is a tax you pay on everything, even within EU, customs is a levy on items imported from abroad.