An abbey church is that is, or was historically, the church of a monastic order. Likewise a friary church is the church of an order of friars. These orders include Benedictines, Cistercians, Augustinians, Franciscans, Dominicans, Jesuits & lots of more. Lots of church buildings of abbey foundation, are or historicallyin the past were, part of a monastic complex that includes dormitories, refectory, cloisters, library, chapter house & other such buildings.
From the first to the early fourth centuries most Christian communities worshipped in private homes, often secretly. Some Roman church buildings, such as the Basilica of San Clemente in Rome, are built directly over the houses where early Christians worshipped. Other early Roman church buildings are built on the sites of Christian martyrdom or at the way in to catacombs where Christians were buried. 
The first very large Christian church buildings were built in Rome & have their origins in the early 4th century, when the Emperor Constantine first legalised Christianity. Several of Rome's largest church buildings, notably Santa Maria Maggiore & San Giovanni in Laterano, have their foundation in the 4th century. It is San Giovanni (St John's) & not the more famous St. Peter's Basilica which is the cathedral church of Rome. St Peter's is also of 4th century foundation, though nothing of that appears above the ground.
When Early Christian Communities began to build church buildings they drew on particular feature of the houses that preceded them, the atrium, or courtyard with a colonnade surrounding it. Most of these atriums have disappeared. A fine example remains at the Basilica of San Clemente in Rome and another was built in the Romanesque period at Sant'Ambrogio, Milan. 
The descendants of these atria may be seen in the huge square cloisters that can be found beside lots of cathedrals, and in the immense colonnaded squares or piazze at the Basilicas of St Peter's in Rome and St Mark's in Venice and the Camposanto (Holy Field) at the Cathedral of Pisa.
