Noodler,
You are 100% correct about I, IV and V being Tonic, Sub-Dominant & Dominant. But because I, IV & V are the "main chords" in the key the terms are also used to describe the functions of all the chords in the key. Here's how it works.
Tonic=Home Base or Rest
Sub-Dominant moves away from Tonic
Dominant returns to Tonic
All of the seven diatonic chords break down into one of these three main functional categories.
The Tonic chords are I, iii and vi.
The Sub-Dominant chords are IV and ii.
The Dominant Chords are V and vii.
The reduction of seven chords into three categories is made possible by the common tones shared by the chords each category. This also makes diatonic substitution possible.
Regards,
Monk
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