This is a hollow root: the middle letter is a vowel (י), so the consonants you really feel are שׂ and ם. The core gesture is putting, placing, setting down. From the simple act of putting something on a table, the family stretches to placing a person in a job (assignment) and to the thing you are set to do (a mission). The hollow shape means the verb conjugates around a long vowel instead of three full consonants, which is why it looks short. Every word here 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.
Hollow roots travel light: only pa'al and a hif'il are in active use here, and the two sit very close in meaning. The passive idea ("to be placed") is normally carried by a separate root, הוצב, rather than by a nif'al or huf'al of שׂ-י-ם. That is typical of weak roots, which rarely fill all seven binyanim.
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.