My employer recently filed Labor Certification for me. Since my wife needs the work permit to work in U.S., can we use the approved Labor Certification for her to work in the United States? or what is the difference between Labor Certification and the Employment Authorization Document (EAD)?

The Labor Certification is an immigration process step. Its goal is to "protect U.S. workers and the U.S. labor market by ensuring that foreign workers seeking immigrant visa classifications are not displacing equally qualified U.S. workers". The Labor Certification is a process of proving that there are no qualified U.S. workers for the position being offered. If there are qualified U.S. workers, then the alien worker cannot be offered the position on a permanent basis. 

The Employment Authorization Document (EAD) gives the alien beneficiary authorization to work for any U.S. employer. The Labor Certification itself does not give the alien beneficiary any work authorization. Also, the alien worker must have a job offer from a U.S. employer in order for the employer to file the Labor Certification.

A U.S. employers file the Labor Certification application at the beginning of the alien employee's immigration process. However, an alien worker file the EAD application for himself/herself and spouse at the last step of the immigration process, with the adjustment of status or Form I-485 application. A Labor Certification is typically for a particular U.S. employer who files the Labor Certification with the Department Of Labor. But an alien worker can use an EAD to work for any U.S. employer. 

Also, the law forbids alien workers from paying any of the costs associated with an Labor Certification, but alien workers are allowed to pay any and all of the costs associated with the EAD application with USCIS.