I need the exact definition and difference between "one of very many" and "one of several". They do not seem to express different amounts!
They don't express specific amounts, but they do express different amounts.
Specifically, one of many would mean a single something inside a much larger group of somethings. For instance:
Patty really wanted the job, but she was just one of many applicants for the position and nothing was guaranteed.
One of several would be a single something within a much smaller number of somethings, since several means around three or four in terms of amount. Such as:
The teacher didn't like many students, but Patty was happy she was one of several whom he respected.
So categorically they're the same, but they mean very different things in usage.