Bluegrass, country and trad jazz can be played "in two" or "in four". Strictly speaking, the tunes in two are related to the march tradition where everything was written "cut time" - 2/2, because a marching soldier has two feet. Marches aren't written in 2/4 because on the fingerbusters you end up with tons of sixteenth notes - write them in 2/2 and a bunch of flags go away from the notation - what would an eighth in 2/4 is now written as a quarter which is a lot easier to read if Maestro Sousa just handed out the hand-copied parts for the march he finished at 1:00 am this morning, and the band is going to sightread the new march at full tempo - "One! Two! One! Two!"
Sometime in the late 20s, jazz players began playing "in four", i.e., twice as many bass notes in the same amount of time. This was highly influential on country music to the point that since the 50s most mainstream country is played in four. The feel difference between four and two is extremely discernible.
Bluegrass has largely remained "in two".
The problem comes when you try to notate it. Younger musicians, especially with a jazz or popular music background, will tend to think "half notes in four", write it in 4/4, and think of traditional bluegrass bass notes as occurring on 1 and 3, with the offbeat chops on 2 and 4 (just like when you're supposed to clap). Older musicians, traditionalists, and those without a lot of theory background, are likely to think "in two" and think of traditional bluegrass bass as playing on 1 and 2 of a measure that contains two beats, and the chops occurring in between those two beats.
In more modern forms of bluegrass, as well as a lot of trad jazz and country, it's quite common to play the first verse and chorus in two, then in four for solos and subsequent choruses with a return to two for later verses.
The thing that drives me nuts is when the tempo is slow, I'm playing in four, and someone says "you're playing it too fast" so I slow down. No, they want me to go into two.