Types of Bills
A bill is a proposed law under consideration by a legislature. A bill does not become law until it is passed by the legislature and, in most cases, approved by the executive. Once a bill has been enacted into law, it is called an act or a statute. It is a law that is unapproved and is not in action, if it is appoved it will be the law, a bill has to go through many stages before this though and that includes the house, senate and president.

There are several types of Bills the House considers such as Government Bills, Members' Bills, Local Bills and Private Bills.

A government bill is a bill introduced into the House of Representatives by a member of Parliament in his or her capacity as a Minister. Government bills deal with matters of public policy.

Members' bill is for members who are not Government ministers, they can put forward bills that are not part of Governments programme.

Local billis promoted by the local authority, it usually becomes a local Act if enacted.

A private bill is a proposal for a law that would apply to a particular individual or group of individuals, or corporate entity. It is promoted by a person or a boby of persons, it becomes price Act if enacted.

For more information on the types of bills check:
http://www.parliament.nz/en-NZ/AboutParl/HowPWorks/Laws/b/a/b/bab4f58d09e143adb06e1751e688ab5c.htm#topTypes of Bills

The key difference between government bills and private member bills are:


The government bill are set in cabinet where agenda goes in agenda. While in private members bill the bill goes in ballot. Therefore this is the key difference is when they get into the House. The government bill has majority votes therefore it is more likely to get in for the bill while the private members bill wouldn't have enough vote in the House. So for the favour of the private members bill the opposite MP would refer to MMP and smaller parties.The Government has a lawmaking programme so that it can act on its policies. As part of this programme, Government bills are prepared for Ministers to introduce to the House.The Government decides the order in which the House will consider Government bills. Private bills are rare. They ask for a change to the law for the benefit of a particular person or group. They may relate to personal or business activities. A private bill’s promoter asks a member of Parliament to take charge of the bill as it passes through the House.

Reference:
http://en.wikipedia.org/wiki/Bill_(proposed_law)Types of Bills