Yes. M1 includes demand deposits (checking, savings, etc) at banks - which includes an awful lot of money banks just made up to lend to their customers. M2 also includes more medium-term deposits like money market funds - which includes even more money banks had loaned to their customers. Then there's M3 - which includes even more bank loaned money that the Federal Reserve doesn't even bother trying to track of anymore.

M0 (or Monetary Base - which is technically slightly different than M0) accounts for only money that are liabilities to the Federal Reserve (i.e. excluding the money banks loaned that they didn't have).

(this is how the U.S. categorizes M0, M1 and M2, though I believe other nations may differ slightly).