Lyxen
Great Old One
By common definition, traveling is any distance at all. By 5e RAW 300 yards qualifies, which could in fact be within a dungeon. By 5e common definition mantra, it's any distance at all.
Here are the common definitions for travel from Meriam Webster.
1. to go on a trip or journey : to go to a place and especially one that is far away.
2. to go through or over (a place) during a trip or journey.
3. to move from one place to another.
Definitions 1 & 2 don't fit the 5e travel section, since 300 feet is all you need to move to travel, so 5e clearly uses definition 3. And again, the travel table on PHB page 182 shows that the travel distances for normal movement are for creatures that move 30 feet a round. Travel and movement are synonymous in 5e. One means the other.
First, I don't take it that way. When I'm exploring a dungeon, moving from room to room, I'm not travelling. Moreover, the group is certainly not travelling, and very probably not as a group, Some people stay put, others scout, then some regroup, there's a fight, etc. None of that is travelling.
There might be some "travelling" being done for example when, having explored the level, the group decides to head back to the stairs, walking as a group. But that is certainly not the norm.
So, clearly, for me, definition one which is the most commonly accepted definition of "travel" (the rules also mention "journey", by the way, which has a connotation of something rather long) is the proper one.
Honestly, between you and me, when adventurers are exploring a dungeon (and I mean really exploring, not moving from one corner of it to another corner ignoring what's on the way), do you ask them if they move at normal, fast or slow pace, and if they used forced march ? No, you use their individual speeds and you take their individual declarations.