Equal to/ Equivalent to/ as much as/ as many as

Equal can mean number. As in "we have an equal number of cats." If you want to talk about number it is important to mention number. This is because we could say something like "People are created equal" which is not number but quality.

Equivalent usually means "the same in quality and could replace" or something like that - it does not have to mean equal in number. As in "9 top European soccer players are equal to 11 American college soccer players." Obviously they are not equal in number, but they are "equivalent" as in interchangeable or balanced. It could also mean the same number but you would need to say "equivalent number."

with "as much as" and "as many as" you are automatically comparing number of extent. You cannot use these to mean that things are equal in quality.

So to recap equal and equivalent can mean number but it has to say number whereas as many as and as much as always mean number or extent.

That is my explanation...