Not sure if you’re aware but the word ranger isn’t so much to do with being at a distance, as it does being on or patrolling a range (think forests, parks). That’s the natural connotation of the term.

Now when we apply that to fantasy, think of Aragorn from Lord of the Rings, or the Night’s Watch from Game of Thrones. Aragorn is introduced as a ranger, while the Night’s Watchmen fit similar duties as keepers of the wall and surrounding land (the range they’re charged with).

The theme of living off the land runs deep in the ranger fantasy, and so it gravitates to wooden bows and weapons with practical survival uses too.