Familiar

Familiars (使い魔) are used by magi.

Magi often withdraw from society into their room to study and rarely come out; thus they need familiars to run their errands. In the end, as they just do the odd jobs, they rarely have more merit than the user. Their fate is tied with that of their master, and receive their assignment from the magus who made them.

To create one, it is possible for the magus to create a fake life with his own Magic Circuits (from his blood, eyeballs, hair), or to capture a spirit from nature.

Ren is the former, created from the corpse of a black cat crossed with the soul of a dead girl. The latter is seldom appreciated since you don't know what spirit it can be. Moreover, it is possible to make a contract with a familiar created by another person, like what Tohno Shiki did.

Therefore, Servants aren't familiars in the original meaning - as they are neither a spirit created by the magus nor a spirit from nature, but souls of dead people that are outside of this space-time axis.

Source: based on the dictionary resource at Jonnobi.