I believe that these special meanings for "signs" and "symptoms", which deviate from their prior meanings in the English language, must have been used for the first time in some influential medical handbook from some important US Medical School, like the Harvard Medical School.
Then they must have spread in USA, and then in some other countries, like Brazil and Norway, which have been mentioned here.
At least France and Germany seem to be among the countries that have kept the traditional terms "objective symptoms" and "subjective symptoms".
Another poster said that "language changes" and this must be accepted. While there are many people who believe this, I do not agree with it. When language changes in order to speak about new things, that is obviously fine. When language changes because someone thinks that the traditional words are not cool any more and they make arbitrary changes in the meanings of the words, that, in my opinion, is lazy and stupid. Every such change in the meaning of the words makes more difficult both the communication with people from distant places, where the meaning changes have not arrived yet, and the understanding of the older writings accumulated during the last centuries, many of which are much more valuable than it is expected by those who read only what was published last year, thinking that the older publications are obsolete. In fact too many recent research papers reinvent things that are decades old, because their authors have not read the old literature.
This change in terminology has been completely random, one could have equally well chosen to use "signs" instead of "subjective symptoms" and "symptoms" instead of "objective symptoms".
So there is no way for someone who has not studied the recent medical terminology to guess what medical doctors mean when they speak about "signs" and "symptoms".
If the author of this terminology would have invented some new words, e.g. "obsyms" and "subsyms", then at least their use would not have caused confusions. Any listeners would have recognized them as unknown words and would have asked for their meaning.