In the world of Fantastic America, magic users recognize the connection to magic in others. There are categories of magic use, but the characters in the story have to figure that out as they go. Miracle workers are fueled entirely by faith, they are calling on their faith to manifest physically. Arcanists use magic to enhance the world around them. While wizards tap into powers of creation and destruction alike.
Miracle workers intuitively invoke their faith to protect or heal themselves and love ones. That is a potent but simple form of magic use. They do not inherently detect magic use in others, but can sense magic use while performing miraculous acts.
Arcanists draw on the ambient magic around them to cast simple spells, concoct potions, build magical artifacts, and set magical wards. While this use of magic is more direct than miracle work, it is less powerful than full wizardry. Still, Arcanists can, with some effort, detect miracle workers and wizards.
Wizards tap into the power of one of six facets of creation. Each kind or school of magic is distinct from the others. The spells, rituals, and inherent abilities of each kind reflect the facet of reality they are empowered by. Wizards can detect wizardry, arcanistry and miracle work on sight. With practice, they can even discern the kind of magic at use.
In practical (or arcane) terms, this means miracle workers can detect magic users sometimes, arcanists can detect magic users with effort, and wizards can read magic use like the label on a can of soup. They may not know what MSG is, but they can learn not to like it when they see it. Arcanists may have just enough warning to get out of the way when something magical is nearby. Miracle workers require a state of faith in action to recognize magic at all.