[lxgr]

A physical card usually uses the number embossed on the plastic on all other channels (i.e. magnetic stripe, chip, contactless) as well.

That's not a hard rule – some cards have no number embossed/printed at all (e.g. the Apple Card), and it's technically possible to use different numbers. But I haven't really seen it done since it could cause quite some confusion, as e.g. some airlines use the card number to look up your online booking at self-check-in machines, which wouldn't work if the two differ.

There are also some special cases of things that are technically regular old smartcards but that do (I believe) use tokenization/DPANs, like wearable form factor contactless payment devices by Swatch or Fidesmo.

[caf]

Ahh, that makes sense - in fact I just used a credit card to pick up linked online Shinkansen bookings from the JR-West ticket machines.

(Those systems all seem to use either magstripe or chip though, so maybe the wireless transaction could still use a different one, in theory).