These three letters carry two threads that braid into one. The first is to rule, to govern, the verb, the ruler, the government all come from it. The second is the mashal: the parable, the proverb, the comparison "this is like that". The bridge is old: to rule and to set a standard others are measured against are two faces of holding authority. Here the rulers and the government cluster on one side; the parable and "comparable" stand a step apart. 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.
Only the pa'al "to rule" is in everyday use. The comparison sense ("to be like") survives mainly in the noun מָשָׁל and the adjective מָשׁוּל rather than as a living verb, so the family leans toward nouns.
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.