Fission, binary fission, cell division: these are all used more or less as synonyms for prokaryotes. "Fission" and "cell division" are more general, because they include mechanisms resulting in more than two resulting cells or an asymmetric division. As a supporting example from the literature, consider this paper:
Angert, E. R. (2005). Alternatives to binary fission in bacteria. Nature Reviews Microbiology, 3(3), 214-224.
Right in the title: "alternatives to binary fission", where binary fission is taken to be the standard prokaryotic division strategy, and in the abstract:
Whereas most prokaryotes rely on binary fission for propagation, many species use alternative mechanisms, which include multiple offspring formation and budding, to reproduce
The same terminology is used for organelles in eukaryotes.
Mitosis itself also involves "fission", and though the term isn't used as often with eukaryotes it does come up in some cases, like in contrasting "fission yeast" (Schizosaccharomyces pombe) from "budding yeast" (Saccharomyces cerevisiae).
Terminology in biology isn't always strictly standardized. Standards tend to proliferate and language itself is not strict. In biology there is a tendency to conform with the terminology others have used in order to keep consistent in the scientific record in which publications build on previous work; there's little motivation to generate a new term to refer specifically to prokaryotic division if existing language used to describe it is sufficient. It's rare that there would be confusion between fission of multicellular organisms like echinoderms and fission in single cells, so there's no need for a separate term. If you're having trouble with your search results, you could try adding other keywords like "bacteria" or "prokaryote" to focus your results, or using excluded keywords with the minus sign, like:
"binary fission" -echinoderm
which on a search engine like Google to only return results without the word "echinoderm" in the result; testing that myself in a Google search only excludes about 10% of the total, though. If you're using Google, I wonder if you've also recently searched things about echinoderms and that's influencing your search results. You can try using another search engine that doesn't track your past like duckduckgo, or using Google's incognito mode to not use your history in your results.