No, this is different from tuning. Most everyone tunes to something called A440 (https://youtu.be/S4R5za6RTX0). All electronic tuners tune to A440 by default. This is not what is meant by the Nashville Number System.
There are 12 total notes in western music. That means a song can be in any of these keys. For fiddle tunes, this key is usually set. For instance, “Whiskey Before Breakfast” is always played in D, “East Tennessee Blues” is played in C, and so on. Banjo tunes are similar–Foggy Mountain Breakdown is played in G. The key that a song is in is called the root, and that root is what is referred to as the 1. The root note of Foggy Mountain would be G, and it’s referred to as the “1”. The root note in Whiskey is a D, and it is referred to as the 1.
There are also all the black notes on the piano that are referred to as flats or sharps. We play and sing in those keys, too, but not as common as some others.
For singing songs, there aren’t standardized keys like fiddle and banjo tunes. What determines the key is the vocal range of the singer/s. For instance, when I sing “Happy Birthday” I’ll do it in the key of G–it fits my voice. But a bass singer may do the same song in C because that key fits his voice.
But whether you sing “Happy Birthday” in G or C, the chord structure never changes. Let me show you. A basic arrangement of chords for Happy Birthday in G are (each letter represents a measure):
G D D G
G C D G
Now, this is in the key of G. G is the root because we’re in the key of G, and G is referred to as the “1” because it is the root. If we referred to the chords as numbers as we would in the Nashville Number System, you would need to know the G major scale:
G A B C D E F# G
1 2 3 4 5 6 7 1
(It’s not spacing right for me, but each number is supposed to reside under the corresponding ordered note. C is the 4, and E is the 6, etc.)
So now we could write the chords with the corresponding numbers instead of letter names, and the chords to “Happy Birthday” would be:
1 5 5 1
1 4 5 1
Do you see what I’ve done?
Now, the reason why that is helpful is because those numbers do not change, no matter what key you’re in. Let’s go back to Mr. Bass Singer who likes to sing this song in C–but, the numbers don’t change! All that changes is the root. Instead of singing in my range of G, we are going to sing in his range of C–C is the root, and C is the new 1. Now, we need to know what the C major scale is to know what chords to play:
C D E F G A B C
1 2 3 4 5 6 7 1
And when we apply our Nashville Number Pattern to the C major scale, we find our chords for Happy Birthday in the key of C are:
C G G C
C F G C
And now, I can take my number pattern for “Happy Birthday” and play in whatever key I’d like, I just have to start on a new 1 for whatever key I’m in.