In English, we use "how many" for countable nouns and "how much" for uncountable nouns. But in Chinese, there's no difference between countable and uncountable when it comes to measure or describe the quantity of something.
We say "how many men" and "how much money" ; both "how many" and "how much" in Chinese is「多少」. "How many men" = 「多少人」; "How much money" = 「多少錢」
「幾」 (adj): a few ; several - Example: 幾個人一齊做 ( a few people do it together)
「幾」 (adv): quite; considerably - Example: 「幾好」( quite good)，「幾快」 ( quite fast)
「幾」 (adv): how; how many / how much ; what
「幾多?」(how many? / how much?)
「幾時?」(what time? = when?)
「(有)幾快?」 (how fast?)
「多少」(how many) is a phrase used to ask or talk about an amount ;「幾」 is mainly an adverb (how / what). For example: 「幾」(how)+「多」(many) = 「幾多」(how many) ; 「幾」(what)+ 「時」(time) = 「幾時」(what time / when)
「多少?」and 「幾多?」only mean " how many?" but 「幾」has other usages.
When should I use 多少 or 几?
When asking [how many of something] or [how much of something] you can use either[多少+(something)]or [幾多+(something)], for example: 多少人 or 幾多人
You can omit 多 in 幾多 in some cases when you want to use a more classical style of speech. Which means you can use: "幾人? " instead of "幾多人?"
Is the difference 多少 and 几 simply "how much" versus "how many"?
The different usages of 多少 and 几 have been explained in the body of this post