Most records will have two sets of numbers.
The most obvious (usually) is the record catalogue number, which is generally on the label, and was used by dealers & buyers when ordering a particular disc.
The other set of numbers is the matrix number, which is usually found in the smooth run-out area (or dead wax) between the label & end of the grooves.
The matrix number was put on the disc by the recording engineers, and each take was given a different matrix.
So, Billy Murray might have recorded the same song 4 times in one day, and each record would be given a number- 1230, 1231, 1232, & 1233.
The powers that be would then select which take they thought was best & they wanted to release, so might say to use 1232.
Larger companies would also add a letter or two, to the matrix number which told them who the recording engineer was that made the recording, what series the artist or song belonged to, or in which city or country the recording was made.
So the matrix on the Billy Murray disc that was pressed might have Bb1232, and indicates that Joe Blow recorded the disc in New York & that take 3 was pressed.
Every record company had their own system or code for the matrix numbers.
Some discs have the matrix & catalogue numbers on the label &/or the run-out area, and sometimes one or both numbers are underneath the label & hard to read. This normally only happens on fairly early discs though.
In short, I guess you could say the matrix number was used by the company for "internal" identification of a recording, and the catalogue number as an "external" identification.
I have no idea though, why a matrix number was called a matrix number, instead of say an "ID" number or a "babbazoozoo" number
Hope I haven't confused you too much
