The oldest image here is pressing a seal into wax or clay to close a document. From that one act three meanings unfold and they all live in the simple verb: to sign (put your mark on it), to seal (close it so no one tampers), and to conclude, finish (the seal is the end of the matter). The causative makes others sign, the passive is for what gets signed, and the action-noun חֲתִימָה covers the signature, the signing, the conclusion, and even a subscription, you "sign on" to it. One root carries you from a wax seal to the last word of a contract. Every word is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Three binyanim work as a clean set: pa'al (you sign), nif'al (it gets signed), hif'il (you get someone else to sign, like a clerk collecting signatures). Pi'el, pu'al, huf'al and hitpa'el are not lexicalized for this root.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.