Mountain-ness. Despite not even being 2 km, Mt Washington's prominence, weather, view, etc all make it more like a mountain, while "mt" Marcy, you can hike in like 3 hours and it's mostly gradual forest trail.

Washington fills the social role of a mountain, it's something you prepare to hike, bring a bag with food and water and a heavy jacket, maybe even microspikes, you check the weather to make sure you're not going to get swept away by 200+ mph gusts, you leave at daybreak so you don't get caught by night during descent, you get to the top and say "This is definitely a mountain", any Adirondack, you walk up casually with zero preparation , not even water and that's it. Maybe you check for avalanche warnings if it's winter.