Yes, but I think you’re mistaken. Climbing a long distance or to a great height is still just climbing, which is a matter of freely moving your character where you want it to go within the game-world. Simply climbing is not meant to be difficult. It’s circumstances you encounter while climbing that can either make the act of climbing itself difficult (like a difficult climbing surface) or pose a threat or obstacle that can make it difficult to make forward progress or not fall.
As a point of reference, here are climb DCs in WotC publications, I verified a couple in OOTA - the narrative for those cases says nothing about any factors in difficulty other than that it's an N foot high climb.
str athletics 10 climb on rope bridge after falling off and catching yourself
str athletics 15 climb 50 foot natural rock cliff
str athletics 15 climb 20 foot natural rock 10' x 10' pit
str athletics 10 climb 10 foot rock wall
str athletics 11 climb 10 foot carved stone pit
str athletics 12 climb 15 foot pit
str athletics 12 climb 10 foot cliff
str athletics 13 climb 10 foot wall with hand holds
str athletics 10 climb 50 foot cliff with hand holds
str athletics 10 climb 30 foot natural rock wall
str athletics 10 climb 100 foot shaft, one check for the whole thing, it's carved by magic
str athletics 11 climb 6 foot natural rock cliff
str athletics 15 climb 30 foot wall 'carved' by a purple worm
str athletics 15 climb 40 foot wall 'carved' by a purple worm
str athletics 15 climb 200 foot slope with 60% grade it is 155 feet high and 126.5 feet long
str athletics 12 climb 40 foot sheer sides of the crevasse
str athletics 10 climb outside of 20 foot diameter metal cage
str athletics 13 climb on metal cage after falling off and catching yourself
str athletics 10 climb 60 foot natural rock cliff
str athletics 10 climb 40 foot natural cliff with hand holds
str athletics 15 climb 2nd floor of lodge timber & plaster construction
str athletics 10 climb 75 feet ice wall with hand holds
str athletics 15 climb 8 foot ice ledge
str athletics 15 climb 9 feet or higher ice ledge with tools
str athletics 14 climb 15 feet around to a ledge