Glad I could help
Yes, as far as I know Search (and Quick Search bar) make use of Apple's Spotlight functionality, which if I remember correctly is turned off by default on networked volumes (apparently, you can enable it using Terminal with AFP shares enabled on the NAS according to sources, although with my 6TB NAS I am kinda reluctant to try, it might take just forever to index), but offers a very quick and advanced search on volumes that Apple's Spotlight supports. Find command, OTOH, just looks through currenct contact sheet the old fashioned way. You can still use it for searching through large amount of files, if you open multiple folders in one contact sheet (be warned that might take a while, especially with NAS, depending on the amount of files).