"Многие магазины" = many (but not all) of the shops;
"Много магазинов" = a lot (a large indefinite number) of shops.
"Много (кого-л./чего-л.)" also can be only a subject or a direct object (because "много" itself lacks any indirect case forms).
No, these are just different "measurement systems".
Многие магазины (many of the shops) refers to the share of the shops (their relative number).
Много магазинов (many shops) refers to the absolute number.
What is more depends on the exact case, the difference is just in the semantical stress (share or absolute number).
For example, if there are 500 shops, we can say многие магазины about 350 shops, but hardly about 50 shops.
However we almost always can say много магазинов about 50 shops, because it's really "many", no matter the share they account for.