"A number of programs" vs. "several programs"

I am always confused between "a number of programs" and "several programs" for saying "many programs". Google Ngrams show that both are widely used terms. Could someone tell me which one should be used when?

Solution 1:

They both mean that more than one thing is involved, but...

• several indicates a small number: "more than a few; an indefinite small number". It falls somewhere between "a few" or "some", and "quite a few".

• a number of tends to imply more uncertainty, or at least flexibility, about the exact number involved. In other words, you see it in places where the count really does not matter:

Problems may be subdivided in any of a number of ways...

...suggested a number of ingenious ways that...

But if you put quite in front of it... "quite a number of" means that the count really does matter, and you are asserting that there are a lot.