Eh, paradigms are different to paths.
Those each correspond to one of the 5 Supernal Realms from which Mages can draw their power.
Those provide you with a perspective on Magic which you interpret in certain ways, and determine your Ruling (easy to cast) Arcana (for which each Path has two, one overt like Space, and one subtle like Mind).
Now, your Mage can interpret that any way they like, but their attitude towards Magic and what they can do will be shaped by their path.
However you can still learn other Arcana, and be just as proficient as any other Path with enough training, and rotes/praxes.
Mages don't need anything to cast. Full stop. They can snap their fingers and try to summon a Ghost from the Underworld. However that's hard. So they instead learn and use Yantras, which call upon the symbols of the Fallen world to bestow them with power from the Supernal.
So they might hold a Candlelight Vigil while summoning the Ghost, with an item it cared for during life, while burning its corpse's Bones.
Similarly, Mages can further enhance certain paths of spellcasting through taking on Shadow Names, or joining Legacies.
e.g.
A Mastigos joins the Legacy of The Strangers, who hide their identities to avoid Fate catching ahold of them. When casting while fully obscured, they can use that as a Yantra.
An Obrimos (Celestial Mage, Forces and Prime) might take the Shadow Name "Seraph", and Angel of Fire. Which means they can gain a bonus when casting any spell in the manner of a Seraph, such as using Forces to take flight, to burn sinners with fire, or to use Prime to ensure people know you speak Truth.
In Mage, you build your own mystic identity more. You're not calling upon a perspective in the consensus, you're accumulating your own array of symbols reflected in the Supernal.