These are pretty general terms for which neither mechanism of action nor regulatory status is relevant. Biocide is a general term that is used most often in reference to synthetic materials having microbial kill (biocidal) effect. Antimicrobials is also a general term that refers to both synthetic and antibiotic materials that have biocidal or biostatic effect. Antibiotic is a more specific term that refers only to materials produced by an organism (esp. a microorganism) and that have biocidal or biostatic effect.
So all biocides and antibiotics are antimicrobials. Not all antimicrobials and, as commonly used, no biocides are antibiotics. Not all antimicrobials are biocides.
Antibiotics are medicines that help stop infections caused by bacteria. They do this by killing the bacteria or by keeping them from copying themselves or reproducing.
Antimicrobials are agents that kill microorganisms or stop their growth. Antimicrobial medicines can be grouped according to the microorganisms they act primarily against. For example, antibiotics are used against bacteria, and antifungals are used against fungi.
Biocide is a chemical substance or microorganism intended to destroy, deter, render harmless, or exert a controlling effect on any harmful organism by chemical or biological means. Biocides are one of the most commonly used techniques in the industry to kill bacteria in the system because of the rapid response.
Well, I see a lot of answers saying that for an agent to be called "biocidal" means it is harmful to organisms. Microbes, even large microbial cultures in a Petri dish, are not an organism. So an agent that is harmful to cell cultures (e.g cancer cell cultures) is strictly speaking NOT (or not yet) biocidal. Right?