I have studied that money is a mass noun, but now I saw that money can be in plural form as well. So I am confused. when we say on something that it's uncountable, then should it not be in one form only? (without singular/ plural - and like water, milk etc.)
In ordinary usage, nouns like "milk" and "water" are uncountable. There are times, however, when such words do have a countable sense. For example, cows produce a different milk than goats. If I want to compare those two milks, then I'm using the word "milk" in a countable sense and phrases like "a different milk" and "those two milks" are natural and sensible.
In financial contexts, it is natural and sensible to talk about different countable monies. The USD and the Euro are two different monies. Taxable income and tax-free income are two different monies.
Strictly speaking, it isn't necessary to force a countable sense onto an uncountable noun. It is just as natural and sensible to talk about "two types of milk" or "two kinds of money", which allows "milk" and "money" to retain their ordinary, uncountable meanings. Your cited definition includes the phrase "as used in financial contexts". A better phrasing might be "as used in financial jargon".
Money is a mass noun, and therefore doesn't NEED a plural form, Garner and The Cambridge Guide to English Usage explain that
Monies is usually used by legal or finance writers to talk about “individual sums” or “discrete sums” of money. That being said,
Monies, and even
Moneys, can technically be used to refer to the plural form of
Money, despite most people disliking it.
Although it makes it more confusing, all rules come with rare exceptions.