The words αυλή and περιαύλι (περιαύλιο) are synonyms.
αυλή is much more common nowadays in modern Greek.
η αυλή του σπιτιού = yard of a house
η αυλή του σχολείου = schoolyard
περιαύλιο is an older form, more formal and it is rarely used nowadays. You are more likely to hear it or read it in a formal context. Most of the times it refers to the yard of a church.
Η δεξίωση έγινε στο περιαύλιο της εκκλησίας. = The reception took place in the yard of the church.