The word klal is used for two very different things.
When Chazal talk about a klal gadol, as they do throughout Shas (and other mekoros following them), they refer to a general rule or principle, often very abstract.
When we talk about doing something “for the klal,” we are speaking about Klal Yisrael, the Jewish people as a collective, not an abstract category but the very human, physical people that make up our religious nation.
Both the theoretical principles of Judaism and the practicalities of how we relate to one another are of central (and general!) importance.
There is a fascinating machlokes (across several Midrashim) as to which pasuk is considered the “klal gadol,” the greatest principle in the Torah.
Rabbi Akiva says it is “Ve’ahavta li’re’acha kamocha” – loving one’s fellow Jew.
Ben Azzai says that it is “Zeh sefer toledos adam” – viewing the Torah as the universal book of all humanity.
Ben Zoma says it is “Shema Yisrael” – our great commitment to faith in Hashem.
And Shimon ben Pazi asserts that it is “Es ha’keves echad ta’aseh va’boker” – centering daily consistency in our avodas Hashem.
These klal gadols teach us complementary messages in our avodas Hashem.