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Traditionally, there are seven rabbinic commandments to be added to the 613 in the Torah: Hallel, Purim, Hanukkah, Eruv, washing hands, lighting Shabbat candles, and saying blessings.
But there are many other requirements decreed by the rabbis over the centuries and found in Mishnah, Talmud, Mishneh Torah, Shulkhan Arukh, etc. Why are they not also considered commandments? Perhaps because they derive logically from the 613? Or because they are not deemed as important (and if so, why?)?
I"ll answer by prefacing a Gemara in Eiruvin 21b that when Shlomo Hamelech instituted Eiruv and Netilas Yadaim a heavenly voice rang out and praised of how wise Shlomo is with these new mitzvos, tosfos asks why didnt this heavenly voice ring out when Shlomo instituted the prohibition of שניות (not marrying ones grandmother etc.), the Chasam Sofer in his responsa answers beautifully that by just creating מצות דרבנן of things "NOT TO DO" does not deserve praise because people can fall through which would make g-d more upset, rather the institution of מצות דרבנן of things "HOW TO DO" thats praiseworthy, therefore Shlomo didnt just prohibit carrying in a מבוי less someone come to carry in a public domain, but rather he told you "HOW" to carry by making a קורה or לחי. Same for נטילת ידים he didnt prohibit rather he said to wash yur hands prior... that is praiseworthy because now people wont transgress those new מצות. Perhaps we can add to answer your question of why we count just those seven mitzvos it is because none of them are prohbitions therefore warrant the praise to stand alone
Most Rabbinic commandments are added details to Biblical commandments. These are the cases where the Rabbis instituted brand-new commandments of their own.
