One idea runs underneath: wholeness, nothing missing. Make something whole and you complete it; settle a debt in full and you pay it; a state with nothing missing is at peace, that is why שָׁלוֹם is the same root. To pay (לְשַׁלֵּם) is literally "to make whole", to give back the full amount. Perfect (מֻשְׁלָם) is "made complete". One root quietly links your greeting, your bill, and your sense of being settled. Every entry 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.
The plain pa'al ("to be complete") is archaic; modern Hebrew carries the meaning through two active binyanim. Pi'el took the "make whole" sense and specialized it into paying, settling a debt in full. Hif'il kept the literal "complete" and added a beautiful idiom: to come to terms with something is to let your inner picture be made whole again. Pu'al / huf'al are not lexicalized here.
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.