Shields appear with armor but seem by the wording to be separate from them. It mentions if you want a higher defense than your armor provides try adding a shield.
This really only matters for the monk. I'm trying to build a spear and shield monk and I want the fast movement if I'm only carrying a shield. What does everyone think?
Shields are not armor for the purposes of stuff like fast movement. However when using a shield and no armor you use the lower proficiency between your unarmored defense and shield proficiency so you will want to get proficiency in shields or it will actulaly make your AC worse. You might consider going fighter with the monk multi-class archetype.