synonyms - Is there a term for "distinguishing between different concepts through the use of different, though synonymous, words"?

Background: A friend mentioned that he wanted to organise a board gaming tournament with 21 players. He opined that there ought to be a way to schedule seven 3-player games so that each player plays each of the seven games, and no player plays any opponent more than once. I replied that there is indeed such a way to schedule games:

ABC DEF GHI JKL MNO PQR STU
SQO ATR DBU GEC JHF MKI PNL
PKF SNI AQL DTO GBR JEU MHC
MER PHU SKC ANF DQI GTL JBO
JTI MBL PEO SHR AKU DNC GQF
GNU JQC MTF PBI SEL AHO DKR
DHL GKO JNR MQU PTC SBF AEI

My friend asked me to explain how I had come up with this scheme. I replied as follows:

"The players are arranged in three cohorts: ADGJMPS, BEHKNQT and CFILORU. The players in the first cohort appear first in each group, the players in the second cohort appear second in each group, and the players in the third cohort appear third. Each round, the players in the first cohort advance one group to the right; the players in the second cohort advance two groups to the right; and the players in the third cohort advance three groups to the right. The crucial reason why this approach works is that 7 is a prime number."

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Question: The substance of my question is as follows. In my reply above, I used the words "cohort" and "group". These terms are synonymous, but I am using them to describe different things in an ad hoc fashion. I am using the term "group" to mean the sets of three letters (players) that are written with no spaces in between, representing players that are playing in the same game in that timetable slot. Meanwhile, I am using "cohort" to mean the three groups of seven players who never face one another because they move "in parallel" between the groups. Even though I am using two words that in principle mean the same thing, I am purposefully lending each of them a technical meaning and distinguishing between two concepts by choosing to describe each of them with one of those ostensibly synonymous words. Is there a term for this practice?

Another examples would be the terms "set" and "group" in pure mathematics (in general English usage these words mean the same thing, yet in mathematics a "group" is a special kind of "set").