If definition.com and thesaurus.com are tracked into the same tracking suite, and are set up as internal urls, then yes, the referrer from definition.com would carry through to thesaurus.com....
But if they are in separate suites, but marked as "internal URLs" of one another (it could happen... not sure why someone would do that, but in theory maybe they only want to see non-company related referrers), then those two sites being in separate suites would not carry over the referrer, and the settings to ignore definition.com as a referrer would not result in no "referrer" being set... no Referrer Instance, no Referrer value (and by extension Referring Domain and Referrer Type, etc). And Typed/Bookmarked also wouldn't trigger because the referrer isn't empty.
@hyder_ziaee advice is good, things change, it's not a bad idea to make sure that the Internal URLs are set correctly...
I've seen people with internal URL set to "." which would result in every single domain in existence to be treated like an internal URL and not trigger a referrer instance...
The other possibility is that you there is .domain.com coded in, which is good.... unless there is a subdomain that has no tracking on it that is sending large amounts of traffic to the site which would then not be picked up...
For instance:
missingtracking.domain.com gets lots of traffic, then sends people to www.domain.com
With no tracking on missingtracking.domain.com to capture the visit, pages views, referrers, etc non of that will be in Adobe to use one the user is sent to the main site... and since the main site has .domain.com set as an internal referrer, the traffic coming from missingtracking.domain.com won't trigger a referrer on the main site....