As noted by @DanF in the comments, משאל and משל aren't tribes in Asher but two names of a city in the territory of Asher, one of a group of cities given to the Levites (see commentators on the verse). Again, as noted by DanF, name variations are not uncommon in Tanach, and in particular in Divrei Hayamim. Several of the Levite cities listed there, for example, are spelled differently or even have completely different names (for example, Tavor-Nahalel) than those listed in Yehoshua.
Rabbi Prof. Shmuel Klein noted in his essay "The Cities of the Kohanim and Levi'im and the Cities of Refuge", pg. 85, that it was a common prose-style by the ancient biblical writers to shorten certain words. Sometimes the reasons for the shortening are more easily understood1, but not always, such as appears to be the case here. With that said, it's also entirely possible that the name simply changed over the centuries (perhaps for a similar reason, that the name was shortened over time because that's how people spoke).
The Encyclopedia Mikra'it (Biblical Encyclopedia), vol. 5, writes on the entry of משאל/משל:
"השם משאל אולי מעיד על כך שהיו שואלים שם באלה-ים; והשווה את שם המקום אשתאול."
Translation: The name "Mish'al" may bear witness to the possibility that they would ask of God there; and compare the place-name "Eshta'ol"."
Perhaps this understanding may connect the name Mish'al to Mashal - in parables, questions are sometimes used. For example:
"He took up his mashal...How can I damn whom God has not damned, How doom when the LORD has not doomed?...Who can count the dust of Jacob, Number the dust-cloud of Israel?..." (Bamidbar 23:7-10)
Da'at Mikra in their commentary on the name Mashal consider it to merely be a short-form of Mishal, and therefore both probably come from turning to God (as stated by the Biblical Encyclopedia).
A possible reason for why the name was shortened may come from the word "שַּׁל" (Shal) which appears in Shmuel 2:6:7, and which many commentators explain to mean "שגגה", which we know means "accidental", but through carelessness. Only people who killed בשגגה - a careless accident - are allowed to escape to the cities of refuge. Perhaps due to its nature as a city of refuge, the city's name eventually changed to reflect the שוגג nature of its inhabitants. Therefore, from משאל (Mishal) to מ-של (Ma-Shal).2 Perhaps it was a form of dark humor among the inhabitants, or perhaps it was meant as a warning to people - be careful, otherwise you'll end up stuck here.
1 For more info, see his essay "מחקרים בפרקי היחס שבספר דברי הימים", pg. 12-16.
2 Metzudat Tzion on Shmuel 2:3:27 compares a couple more words of the same root.