Nuns live in monasteries. Sisters live in convents. Nuns usually
spend their entire lives in the monastery where they work and pray.
Sisters live in a convent but perform most of their work outside
the convent - schools, hospitals, etc.
Convent when they ARE nuns, abbey when they are STUDYING to be
Actually, nuns, strictly speaking are monastic women in solemn
vows. They live in a monastery. A convent can refer to any building
or buildings where religious women live; or in past times, friars.
Now it would mostly refer to communities of sisters as opposed to
nuns. Abbey refers to a canonically erected monastery with a
minimum number of religious.
Nuns originally lived in convents or monasteries and many continue
to do so today. Others have become more secular in recent years and
may live in shared homes or apartments.