The old sense of these letters is to get across: to ford a river, to come out the other side. From crossing came succeeding, because to pull a thing off is to get through it. The verb gives you both the simple act and the causative push; the nouns give you success itself, the lucky one, and, in a curious twist, the flat plate and the little flask. When you wish someone בְּהַצְלָחָה, you are wishing them a good crossing. 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.
In daily speech the hif'il לְהַצְלִיחַ has all but replaced the older pa'al: a modern speaker says הִצְלַחְתִּי ("I succeeded") far more than צָלַחְתִּי. The plain pa'al survives mainly in the literal sense of crossing. No passive or reflexive partners are 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.