As a lawful permanent resident (“LPR”) holder you can qualify for Citizen if you have lived and worked in the United States for a minimum of five years. Once you have satisfied the five year requirement you may qualify for Indefinite Leave to remain in the United States as a citizen.
H1B: For graduate level workers usually with at least a bachelors degree or equivalent coming to the US to take a job in a specialty occupation, or to undertake specialist research for the US government’s Department of Defence, or for successful fashion models. When the US economy is doing well there is a serious shortage of visas. Currently the visas run out within a few days of becoming available in the beginnint of April each year.
H2B visas: For workers coming to the US to fill a temporary or seasonal shortage that is not in the agricultural sector. The employer must apply to USCIS for permission to employ migrants on this visa.