To expand a little bit, a vaccine contains a substance, often a specific protein, a viral capsid, or k illed/attenuated bacteria, which the human body recognizes as a pathogen. The immune system then mounts a response by creating antibodies and memory immune cells, which primes the system to appropriately and effectively mount a rapid immune response to eliminate the pathogen when it comes for real.
We can observe and measure the effects of a vaccine in the body. We can, and do, test for antibody production. I had some titers last year to verify that I had antibodies for measles, mumps, varicella, tetanus, etc. I didn't have any antibodies to mumps, so I had to get another MMR vaccine, and afterwards I had the antibodies. I was not immune to mumps, then I got a vaccine and now I am.
By contrast, homeopathic preparations contain literally no substances other than the dilutant (typically sugar, water, or alcohol). Homeopathic preparers take nonstandardized substances, such as a plant extract containing unknown and undstandardized quantities of who knows what, and serially dilutes them in water etc. After 10-100 dilutions, the final preparation typically contains none of the original substance at all.
Homeopathic preparations have no known or even theoretical mechanism of possible action. Indeed, the entire idea of homeopathy is directly contradictory to everything we know about biology, pharmacology, and physics.
Note that this is in contrast to herbal or natural remedies, which, while unstandardized and often not thoroughly tested, are biologically plausible.