When two (or more) Christian Churches (denominations) enter into the formal relationship known as "Full Communion," it means that they mutually recognize each other as true Churches of Jesus Christ, possessing all essentials for living and working faithfully in Jesus' Name.
These churches permit their members to move back and forth freely, without being required to undergo rebaptism or reconfirmation---they are recognized as already part of the larger fellowship which Full Communion provides.
These churches also provide for the orderly exchange of clergy, both for temporary service, and for permanent transfer, as appropriate, while recognizing that each other's clergy may minister to each other's members in orderly, approved ways. (Today, it is not unusual to see an Episcopal priest serving as pastor of a Lutheran [Evangelical Lutheran Church in America] congregation or vice versa, and so in other denominations.
The listing on our home page shows those denominations (churches) with which we have relationships of Full Communion. So if you're a member of one of these denominations, you should know that you are fully welcome at Pilgrims' and will be treated as one of our own members---and should you wish to become a member of Pilgrims' it's as easy as saying "Sign me up."
There is, however, one thing yet to be said. These formal relationships are very specific. For example, the United Church of Christ (UCC) is in Full Communion with the Evangelical Lutheran Church in America (ELCA). The ELCA is in Full Communion with the Episcopal Church in the USA (ECUSA); however, the UCC and ECUSA are NOT in Full Communion with each other---yet!