I’ve seen all three translated as ‘receipt’. Are they synonyms? Or are there subtle differences in meaning to trap the unwary traveller?
It is an area where English usage is very sloppy and nearly everything works by context except in the most formal of instances.
@coljay, in informal speech, they might all be used more or less interchangeably, but there are differences 
Fatura is an invoice, which details the provided goods or services. Recibo is a receipt, which serves as proof of payment of said goods/services. If combined in a single document, they become a fatura-recibo. Talão is typically used either to refer to a receipt (like recibo) or a coupon, but not to an invoice.