In the Online edition of the Encylopedia Britannica, their article on the Eucharist (also called Holy Communion or Lord’s Supper) says:
Furthermore, different denominations disagree on whether access to the
Eucharist should be open to all Christians or restricted to members
who have fulfilled initiation requirements and thus are in full
communion with a particular church. Among Baptists, for example, the
practice of “close communion” has restricted the ordinance to those
who are baptized properly—i.e., as adults upon a profession of faith.
As a result of such variations, the Eucharist has been a central issue
in the discussions and deliberations of the ecumenical movement.
Searching Google itself shows that the basic principle remains today in many churches -- while a church may recognize the Baptism of a person, that does not automatically mean that you are entitled to take communion in any other Christian Church. For instance, someone confirmed in the Episcopal Church will not automatically be entitled to take communion while visiting a Catholic congregation; each denomination has its own requirements for what a candidate has to meet before they can take communion with that church.
For an overview of the issues involved where the Baptist church differs from other Christian denominations, see the article Believer's Baptism at baptisthistory.org. Author William H. Brackney says:
Like their brothers and sisters elsewhere, Baptists in the United
States also perfected the practice of believer’s baptism by immersion.
Early colonial Baptists in New England followed English and Welsh
Baptist precedents by baptizing only believers, while ensuring that it
was a voluntary act of faith and not a routine of church membership.
Later in the United States, Baptists used the ordinance of baptism to
demonstrate their faith publicly. Some churches baptized candidates as
conversions occurred or a catechetical class was finished. After
revival meetings or special evangelistic outreach, many candidates
were often baptized together. Some churches followed the ancient
practice of holding baptismal services at Easter to identify with
Resurrection Day, while in other cases several congregations joined
together for combined baptisms.
Brackney also says:
Another recent issue that has energized some Baptists is whether
baptism should be required before a congregation approves full
membership. Traditionally, this has been the understanding of most
Baptists. However, in the late 1700s, some British Baptists began to
argue for "open communion," by which they meant that they invited all
who followed Christ to celebrate the Lord’s Supper. Later in the
1800s, British and American Baptists were influenced by participation
in the ecumenical movement, and some congregations began to practice
"open membership." These churches allow persons who are professing
Christians to be given all the rights and privileges of church
membership without having been baptized as believers (assuming they
were baptized as infants).
Brackney also says that "Baptists have written more books on this subject [i.e. Baptism] than on any other topic." and a search of Google Books bears him out. A search for the phrase "full communion" and "Baptists" in Google Books turns up many histories and publications of the early Baptist Church in the USA where the requirements for being in "full communion" with the church were hotly debated.
Finding out the precise requirements of the Pittstown Baptist Church may take a little digging (the answer might be in some of the other records on the CD-ROM you linked to). But I think it's pretty safe to assume that a Baptist church of that era would not have practiced infant baptism. To be considered a full member of the community, entitled to take communion, would probably have required a profession of faith and an immersion baptism. The question remains -- at what age would the candidate have been considered old enough to give a confession of faith?
If the two references you cite by name are the same person, then Edward Penny would have been in his late forties -- almost fifty years old -- when he was admitted into full communion with the church.
I would gather any other clues that I could about other members of this congregation, including the ones who were named in that same entry, to see if I could find a pattern for the practices of this particular church. Searching for a history of the church might yield other clues.