Note - this is a long technical post, nerdy inclinations or a strong coffee required 
@Frnk, you have it all pretty close with Application Selection. EMVCo Book 4 Section 11.3 for the gory technical details.
The card supports „A, B, C“, and the POS device (terminal) supports „B, F, G, A“. The terminal compares what it supports with what the card supports, creates a short list (candidate list), orders this by the priority set by the Issuer (A first, then B, then C), and if there is more than one entry in the candidate list, prompts the cardholder to pick one.
Getting the cardholder to choose which „payment application“ they want to use can be a UX nightmare (from my experience). I had a quick look this morning in the „dead test card box“, and this is the least scary proposition.
In a previous life, we had test cards, which were not representative of the real world, to test things like scrolling down long lists, or going to a second page. Fun times…
There is quite some work done behind the scenes that ensure the selection by the terminal of the correct payment application on the card is silent and without cardholder interaction. Domestic schemes (like Girocard or the various US schemes) can ensure that if the card and terminal both support the domestic scheme, that is what is chosen, even if there are other options.
My Google-Fu is failing me this morning. In Finland and Belgium, there were cards issued that were both „Credit and Debit“ - an embossed card number on the front (credit), and a printed one on the back (debit). This is the closest I can find (Cards - Danske Bank) which has the functions. As a customer with this kind of card, you can get prompted for „Credit“ and „Debit“ at many POS devices.
The POS device/terminal just consumes the data that comes on the card, and so the decision is highly driven by the choices made by the Issuer. My wife’s VR Bank card supports the following payment applications (these are called Application Identifiers - AID for shorthand). The terminal reads a bundle of data from the card, and below is a subset for readability.
A0000000032010 - Display Name „V PAY“ - Priority 02
A0000000032020 - Display Name „V PAY“ - Priority 01
A0000003591010028001 - Display Name „girocard“ - Priority 01
D27600002547410100 - Display Name „girocard“ - Priority 01
The AID (RID+PIX) system is managed by the International Standards Organisation (www.iso.ch) under ISO7816 Part 5 (ISO 7816 – Wikipedia).
In Germany, as you note above, the „girocard“ application is selected for this card, while outside Germany, one of the VPAYs will be chosen. In the majority of devices supporting VPAY, for this card, a cardholder will be prompted to pick „VPAY“ or „VPAY“, even though the AID for Priority 02 is actually Visa Electron.
Supporting both VPAY and Visa Electron on the same card (actually pointing to the same content) means that your acceptance internationally will be better. For a while (2010-2016) VPAY was not very well accepted, although I’m assured by colleagues that it’s much better these days.
The payment applications offered by the card can be different over the chip and the contactless interfaces. Tapping is finely tuned (generally) to avoid the need for the cardholder to do anything, except enter their PIN for higher value transactions.
Double tap - for a range of more complex interactions like cardholder selection - can be very messy. In the case of the Finnish/Belgian cards I mention above, the issuer would offer Credit and Debit over the chip and probably debit only over contactless. That makes the cardholder experience less prone to confusion.
Edit #1 - spelling
hatte ich oft Probleme. Dass die Sparkassen Automaten die Visa/V-Pay Kombination noch nicht unterstützen macht mich nicht optimistischer. Ich bin gespannt auf die kommenden Erfahrungsberichte hier im Forum!
