From a genealogical standpoint, the idea of "geographic location" involves two distinct systems. The first can be summarized as a global positioning system (GPS) that can identify the exact location anyplace on the surface of the earth. The second, completely different system, involves identifying the location of an event in relation to its geopolitical location over time. For example, if I were to state the location where my father was born, I could say he was born in St. Johns, Apache, Arizona, United States (or USA) or I could also say he was born at 34.507118, -109.363181.
In the first instance, the geopolitical location, the "location" would have changed over time. Each of the designated locations would have been different at different times. St. Johns was first used anciently as a crossing of the Little Colorado River as was called Tsézhin Deezʼáhí in Navajo. Later, it was called El Vadito in Spanish. The next name for the town was also in Spanish, "San Juan." The first building, a stone house, was built in 1874. Another small town was built beginning in about 1879 named Salem. Eventually, the entire community became known as Saint Johns or St. Johns (with an "s"). The two ways of spelling the name of the town are somewhat arbitrarily used depending on the context. The official website of the location uses the spelling, "St. Johns."
The town is also presently located in Apache County. However, when the first settlement was made about 1874, Arizona had been a territory of the United States of America since Monday, February 23, 1863. At that time there were no counties. The first county that contained what would become St. Johns, was Yavapai County formed on Wednesday, November 9, 1864. The townsite became part of Apache County on Thursday, February 13, 1879. So, technically, the first house was built in Yavapai County. Arizona became a state on February 14, 1912. So, depending on my father's birthdate, he could have been born in Arizona Territory or the State of Arizona. But in either case, the location of his birth by geocoordinates would not have changed.
What has all this got to do with British Colonial America? Well, genealogists have for some time now had a rule that the place of an event in a person's life should be recorded as it was designated at the time of the event. As you can see from this very short example, place names change over time as do the jurisdictions to which any particular locations belongs. This is the case because of the simple fact that genealogically significant records are created at or near the place that an event occurs and recorded either by someone who witnesses the event or has some duty to report the event. So depending on the place and the time period, a genealogist would start looking for significant records from the jurisdictions in force at the time the events occurred.
Of course, genealogically significant records can move around (not by themselves but by those who claim ownership or whatever to the records). In many cases, notwithstanding the movement of records, the identity of a person can only be known by establishing the EXACT location of an event in the person's life.
So what about using the designation of "British Colonial America?" First of all, there is no such place and secondly, there is no firm time period for the non-existent entity existence. Here is one almost definition from Wikipedia: British America.
British America refers to the British Empire's colonial territories in America from 1607 to 1783. These colonies were formally known as British America and the British West Indies before the Thirteen Colonies declared their independence in the American Revolutionary War (1775–1783) and formed the United States of America.When did the United States of America officially become an independent country? Certainly not in 1776. How about 1783? How about 1789? By the way, Canada was a British Colony and arguably part of British Colonial America ( What is America anyway? Does America include Hawaii?) and Canada was a British Colony until when? Canadian history is even more complicated than some of the history of the United States of America and what if you were born in North Carolina in 1863?
Let's just say that deciding on a particular name for a country can be more complicated than most can imagine. Most politically inspired names of locations are somewhat slippery. There are some genealogists who routinely use "British Colonial America" for any event that occurred in one or more of the colonies up until 1776. On the other hand, there are those who resent that usage and have their own designation.
I have long been an advocate of using geographic coordinates to identify exact locations and then using historical narrative, like my discussion above about St. Johns, to identify the possible location of records assuming the researcher can identify the time period in question.
More about this as time goes on.