Over here in Poland, companies usually require a "proof of purchase", which can be a receipt or an invoice. As a buyer, it's up to you which one you want to receive[0]. There's a special kind of pseudo-invoice called "personal invoice", which is like a VAT invoice except you don't need to be a company or provide a tax ID for it. This is the one you want in any scenario when you expect to hold on to the proof of purchase for longer than it takes to reach the nearest trash can - its killer feature is that it can't possibly fit on a thermal paper receipt[1], so you get it printed out using regular, durable means, on regular office paper (and/or e-mailed as PDF).

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[0] - On-line you usually get to pick at check-out, off-line you usually have to ask before paying.

[1] - Technically it could, but it would be quite an achievement, and it's sufficiently non-standard that nobody bothers.