Domain availability asks whether a registrar or registry currently allows registration of a particular internet address. It is a technical and commercial lookup for a spelling and extension. The answer can change as registrations change, and the provider's checkout is the place to confirm a purchase.
Trademark availability is a different legal question. It can involve existing marks, related goods and services, geography, priority and the likelihood of confusion. A domain search does not resolve those factors, and a domain owner does not automatically own trademark rights to the words.
Search relevant trademark databases and business records for the markets where a brand will operate. Consider similar spellings and pronunciations, not only exact matches. Seek qualified legal advice for a consequential launch or when a search raises questions.
Use a domain check as one part of naming research. Do not treat an available address as proof that a brand is legally clear, exclusive or safe to use.