That is not correct. The float is the number of shares that are actually issued minus the amount of shares held by insiders. The authorized shares are the maximum a company can issue and it can be raised.
For example XYZ company is allowed to issue 500 million shares. The 500 million is the authorized count. Say there are 150 million outstanding and the float is 125 million. That means there are 125 million shares available (the float in this case) to the public for trading and 25 million shares are held by insiders which are usually institutions or in the case of most penny stocks, people in the company.
No, you're getting restricted and authorized confused. Authorized is the amount that the company is permitted to issue. So if they have an authorized of 1M, they can't make the o/s more than that (unless they are a NV corp - but we won't get into that here). Outstanding is the total amount owned by shareholders - this includes restricted shares. Float is the difference between the restricted and the o/s (not the authorized).