manche is used for countable things (e.g. manche Mädchen "some girls")
etwas is used for uncountable things (e.g. etwas Wasser "some water")
It may help to think of etwas as "a little bit of" -- you can have "a little bit of water" but you can't have "a little bit of girls".
Dictionary suggestions can be misleading when they do not fit the meaning of the word in a specific sentence. However there are several different meanings attached to "manche" depending on context. "Manch ein Mädchen" would mean "many a girl", "so manche Mädchen" is idiomatic and closer to "many girls" and "several girls". As used here, on its own, "manche" is more closely translated as "some" or "a few".
It's also used with uncountable/mass nouns which are singular, e.g. mancher Wein "some wine (some quantities of wine)".
And sometimes even with countable singular nouns, especially together with "so", in the sense "many a": so mancher Schüler hat schon... "many a student has already...".
Few would be "paar", and is limited in quantity. "Some" (manche) is like "much" (viele) and is not countable:
"Some stars are blue and some are red." (That could be in the billions or trillions) "Some girls eat rice." (On the planet, that would be in the billions or trillions)
But, "A few stars are blue and a few are red." (that's just a few distinct stars.) "a few girls eat rice." (and a limited number of girls.) This changes the amount of subjects.
Wenige, einige, manche, ettliche, viele and alle are used in the plural. There is no difference: manche Frauen, manche Männer, manche Kinder, viele Frauen, viele Männer, viele Kinder. Only the word "manch" can be used with nouns in the singular: manche (or manch eine) Frau, mancher (or manch ein) Mann, manches (or manch ein) Kind. Words for the quantity like etwas and viel are used in the singular but don't change: etwas Wasser (das), etwas Milch (die), etwas Wein (der), viel Wasser, viel Milch, viel Wein.