Gives one reason among others, often implying there are additional unstated reasons. Usually indicates one of several reasons.
the thing is; for one thing
Used at the end of a sentence to give a reason for an unstated but deducible conclusion. Often softens a statement or implies 'you know'.
Well, I'm busy too, you know.
It's raining, and on top of that the wind is strong.
He is kind, and funny, so he is popular.
It's started raining, and (for that and other reasons) let's not go out today.
もう遅いし、帰ろう。
It's late, so let's go home (implying that's a good enough reason).
I'm busy, so (among other reasons) I can't go today.
Today's a day off, so let's go somewhere.
Well, it's expensive, you know.
ので is a formal, neutral way to give a reason, whereas し is conversational and often implies additional unstated reasons.
し lists parallel reasons or facts (often more than one), while て simply connects two actions or states without that enumerative nuance.
Derived from the classical Japanese auxiliary verb き (ki) or the conclusive form of verbs, evolving into a conjunctive particle. The exact historical derivation is uncertain, but it has been used as a listing and reasoning particle since early modern Japanese.