A published patent refers to the publication of a patent application, which is be reviewed by the Patent Authority (USPTO, EPO, JPTO, etc.). Once the merits of the application are acknowledged by the Examiner, process which takes from about to 2 to 4 years, the patent is granted (issued). The difference is that a patent application does not protect the inventor from any potential infraction to his/her inventive matter, and the inventor is allowed to start civil actions against the infractor, only once the patent is granted.

Does the government proviide money grants for patent application work done by patent lawyers

There are no requirements to prove anything to get a patent. Under US law, there is a constitutional right to have a patent that properly claims a qualifying invention.

The patent office must prove that the application or the invention does not qualify under one or more laws or rules if it wants to reject an application for a patent.

If you want to get a patent for your cool invention, you need to file a design, utility or plant patent application to the government. You can also file this application electronically.

The website of the United States Patent and Trademark Office links to a patent application form in PDF format. The link is about half-way down the page, under "provisional application for patent..." http://www.uspto.gov/patents/resources/types/provapp.jsp