What is the relation between the First Baptist Church and the Baptist Church? In my neighborhood there has been a Baptist Church for a while. I'm moderately aware of the history of Baptist Church in general.

Very recently a temple of The First Baptist Church has been built. I´m wondering about two things: first, what is the history of the First Baptist Church? Second, what are the main differences between the First Baptist Church and the Baptist Church?
Some baptists have the tradition of naming the first Baptist church in a city or other area "First Baptist Church".  Sometimes this numbering even continues; for example, in my area there is a "Fourth Baptist Church".  I do not think there is a denomination or association called "First Baptist", as it is merely a naming tradition.

You should also be aware that there are perhaps over a thousand Baptist denominations and associations. In the United States, two of the larger ones are the Southern Baptist Convention and the American Baptist Conference.  They have somewhat different beliefs and practices.