I can’t comment on where CoL and EoL themselves source their data from, but as far as I know, the iNat tool only searches those 2. It may be that if EoL sources or imports data from Wikidata, then in a sense it is a source, but it is not directly searched as far as I know.
this used to be a more useful tool back before the new taxon frameworks. If a taxon wasn’t in the iNat database, you could just “search external” and have it brought in. The problem now, is that iNat uses PoWO for plants, for instance, so it’s not always appropriate to be pulling names through from those (different) external sources. I know one of them is still accessing an old version, and there are no plans to update to the current because of the frameworks.