They’re the same. Marihuana is based on previous federal acts.
CRA ND, Cannabis Regulatory Agency, “Why is marijuana sometimes spelled with an "h" and other times spelled with a "j"?” https://www.michigan.gov/cra/faq/licensing-list/additional-new/why-is-marijuana-sometimes-spelled-with-an-h-and-other-times-spelled-with-a-j, kav
The Cannabis Regulatory Agency (CRA) is frequently asked why marijuana is sometimes spelled with a “h” and other times is spelled with a ”j.” Both spellings – marijuana and marihuana – are acceptable. To avoid confusion, many in the industry refer to the botanical plant — cannabis. While the spelling with a “j” is more common today, you will still see Michigan law using the “h” spelling.
The spelling of marijuana has a long history in the United States. Michigan’s history primarily starts from the spelling that was chosen for the Marihuana Tax Act of 1937. Michigan adopted its statutory definition of marijuana in the Public Health Code, utilizing the past federal spelling, marihuana.