Certifications Mehadrin and Badatz both point to a higher tier of kosher supervision that goes beyond the basic standard. Mehadrin means the agency followed the stricter opinion at each step, and Badatz refers to a rabbinical court whose certification is usually held at that mehadrin level. Neither one means a regular hechsher is unreliable.
Certifications Glatt kosher means the lungs of a kosher animal were found completely smooth, with no adhesions that needed closer inspection. It is not a different kind of kosher. It is a stricter threshold within kosher meat, and here is what that really tells you at the counter.