I guess you're "or" didn't mean one or the other [label] but that either label for that music clip would be appropriate. Is that right?

Azizi, as mentioned above, the term "Dixieland jazz" is often used (perhaps loosely) for what in the UK many people call "trad jazz". I think the latter term (short for "traditional" - aargh!) was used in the 1950s onwards (or possibly even earlier? someone will know) to distinguish it from "modern" jazz (I leave it to others to define that!)

If you accept that "Dixieland" is more or less interchangeable with "trad" then the answer to your question is "yes". However the Cap'n and others have distinguished between "Dixieland" and "New Orleans" jazz, so it might depend on whether all "trad" jazz can be strictly called "Dixieland" - possibly not, but many people do use the terms as interchangeable, rightly or wrongly.