Great Old One
You're entire argument boils down to a very broad and vague rule that says, "5e usually uses the common definition of things." to overrule the very specific rules that say that travel is based on racial movement. The game doesn't work that way. Specific beats general, not the other way around.
I don't deny that there is a rule about travelling, what I'm saying is that it does not apply to exploration in general. What I'm saying is that (and it's always been that way, whatever the edition), it goes along the lines of:
- DM: "You enter the tomb, what do you do ?"
- P1: "I go to the door at the end of the room and listen."
- P2: "I stay by the exit and draw a quick map."
- P3: "I go to the sarcophagus and inspect it"
- DM: "There is some noise down the passage at the other end of the room"
- P1: "I whisper to the others that I'm going to scout, and I stealthily go down the passage."
What might happen is that, sometimes, it might go along the lines of:
- P1: "We need to go back to the entrance" or "we are travelling to the next town"
- DM: "OK, do you have a marching order, are you doing something special while you travel?"
Are your games different from the above ?