When Is Hacking Illegal and Legal?

"The White Hat Hackers are those hackers who look for backdoors in the software when they are legally permitted to do so."

The job of a hacker isn't to look for backdoors in software. There maybe cases where they have specifically been hired to look for "backdoors" but this is not the general terminology you should be using.

"The Grey Hat Hackers are those hackers who are like Black Hat hackers but do not hack to cause any damage to any organization or people’s personal information or data. They are hired by companies or organizations to hack into their computer system and notify the administration if their order has any vulnerabilities. This is done so that these organizations can further secure their networks. Software companies make use of such hackers and hacking processes."

Grey Hat hackers are not hired by companies, or if they are they wouldn't advertise themselves as being grey hat.

"There are many ways in which the process of hacking could be explained. It could be described as a breach of the system or unauthorized access. Still, hacking is an unwarranted attempt to infiltrate a computer or any other electronic system to attain information about something or someone."

Hacking is not defined only as breaching a system via unauthorized access. There are many examples of legal hacking.