All colleges offer 2 tracks for science classes: one for science majors; one for everyone else. Some colleges offer three tracks for sciences classes: one for science majors; one for allied health sciences** majors; and one for arts/humanities/business/social science majors. Only those classes that a science major would take fulfill admission requirements for medical school.
**nursing, nutrition & dietetics, athletic training, emergency medical services, dental hygiene, speech & language pathology, etc.
Public health majors often take the allied health science track classes. These classes are not a rigorous as those offered for science majors and may be substantively different in the content/topics covered.
Non-science major track classes, as @thumper1 mentions, are elective science classes that humanities or social majors take to fulfill their GE science requirements. Astronomy for Star Lovers, Intro geology (Rock for Jocks), Biology for the Non-major, etc. These courses count as fulfilling any science GE requirements for graduation for non science majors, but will not earn credits for a science major.
Med schools are moving toward competency based admission requirements as part of a LCME initiative. About half of med schools already use competency based admission standards. Although these new standards no longer require specific classes, each school has a list of "strongly recommended" coursework it expects all applicants to have completed. The burden of proof is now on the applicant to demonstrate a high level of competence in each of the broad competency areas the med school lists. (e.g. biological sciences, genetics, general & organic chemistry, biochemistry, physics, statistics, written communication, etc) You can do this through coursework (easiest to do) or through alternative pathways--like substantial, in-depth research or having publications.
For medical school, you can pretty assume that "strongly recommended" or "recommended" means required--or else you better have a damned good reason why not and something even better on your record.