One reason I can see is not actually wanting the difference to be seen as small as possible. When you are in the same church and making every effort to preserve the unity of the Spirit then there is no advantage to adding confusion. But when you have already split. Then you have to justify that split. So you look at faith. Bryan Cross says:
Just a quick point of clarification. The Reformed conception of faith is not intellectual assent, but fiduciary faith. (Fiduciary faith is a novelty, something unknown before the sixteenth century.) From a Catholic point of view, fiduciary faith is a conflation of the theological virtues of faith and hope.So why does Calvin use the term "faith" in a new way? He has split the church over the slogan "faith alone". With further reflection he might come to think it is not faith alone but rather faith and hope alone. But that would be a huge admission of defeat. That the slogan of the reformers is wrong and they are moving to a more Catholic position even if they are still not completely at the Catholic idea of faith, hope, and love. I can see how it is rhetorically much more attractive to "clarify" what you really mean by faith. People play with words to avoid admitting a mistake.
This is why schisms are so hard to fix. Even when the substance of the schism has been reduced by the spirit working on both parties you have a lot more pride involved. It would be diffcult for Calvin to admit that he claimed huge spiritual authority without adequate justification. So he has a vested interest in making that theolgical difference seem large. If he was arguing from within the church then he would likely have limits on his teaching that he would want to have removed. So the incentive would be to make the differences seem as small as possible.
The opposite temptation can be seen on the Eucharist. David Anders says:
However, I completely agree that these very same terms – real, substantial, local – are given a different signification in Catholic theology. Knowing that, Calvin can be accused of some dissimulation for using terms that had already acquired a technical precision in the academic theology of his day.But the point is why would Calvin engage in this dissimulation? On this issue there were many ideas out there. Luther and Zwingli were fighting each other. Calvin seemed to look for middle ground. Even then he saw that if the reformers didn't unite around one faith then nobody should believe they had the truth. So word games are used to try and avoid schism not with Catholics but with other protestants. That seems like a noble goal. The trouble is that covering differences with carefully chosen words is no way to deal with them. Look at the Anglican church if you doubt that.
So both the fact of schism and the threat of schsim tend to cause us to change our language and not deal honestly with our theological opinions. What we need is unity that does not depend on uniform theological opinions. A unity that depends on obedience to something higher than someone else's theological opinion. When that is established then we don't need to play these politcal games.