No, movement is movement. Mixing up words which are used specifically in the rules (just as not seeing the difference between one character and the group) is just proof that you don't understand them and mix things up.
Once more, by all means, play the game the way you like, but if you want to discuss them, please read them properly.
And yet, it has its own section, because travelling is not movement, it's travelling. It's not movement, it's at best a subset of movement, it's not exploration, it's not social and it's not combat. It's an edge case, and a very small at that, since travelling is, in general, boring.
Of course, because it's a well designed game, the small subset of travelling uses the same rules as the rest of the game (although applying to a group rather than to adventurers individually, just read the rules). Does it mean that it's general rules ? No, because it's just a small subset, lost in a subcategory of movement.
You are not qualified to speak about the intent of the rules, as demonstrated many times before.
And as a player, I would not play in your campaigns where you rob characters of vital rolls on the spurious principle that, as soon as they breathe, they are travelling....