Many times there is a relationship, but the two do not have to be related. Each process is different or independent. If you qualify, you may apply for a green card with or without an H-1B. Sometimes they seem related because many employees who obtain a green card through an employer have also had an H-1B through the same employer, but that is not always the case.
If you have any questions regarding immigration, please feel free to call me, immigration attorney Shawn Mesa at (813) 679-5780.
Disclaimer: This information is provided as a public service and not intended to establish an attorney-client relationship. Any reliance on this information is taken at your own risk.