It helps me to think of it like this: The Church - both visible and invisible - has gone by different names in different times. It was once called Israel (and Judah), the nation being the visible church containing most of the invisible church.

Jesus' work hugely multiplied the scope of the Church by extending it beyond the national and/or genetic borders of Israel, and under His administration we call it "the Church." At no time did one "replace" the other in any sense.