These are very similar and broadly overlapping terms. Microbiota is used to refer to the microorganisms that are associated with a host, while microbiome is a wider term that covers the host-associated microorganisms as well as their genomes, enzymes, metabolites, and their environment. If you just want to talk about the gut microbes, you can use microbiota.

Thank you Dr. Bik (or Elisabeth), everything is clear now. Csaba

Microbiota is the appropriate word.