I use Finder's Search bar a lot to find specific items nested in my folders. It usually works flawlessly and I find all the items I want. Other times it just doesn't do anything:
Imagine a folder with just 10 files, and one of the is an image ending with .png. If you search .png in the search bar, Finder literally doesn't find it!
This happens to me maybe once every couple days. I'm not sure why - relaunching Finder doesn't seem to help either.
Indeed, the Finder fails to live up to its name in my experience as well. Results seem so frustratingly random as to what is found and what is missed.
Beware of one setting that may help: Finder > Preferences > Advanced > "When performing a search` with a popup menu offering "Search this Mac", "Search the Current Folder", "Use the Previous Search Scope".
Beware of the "Search" bar with scope filter buttons that appears when typing search criteria into the upper-right corner.
Finding the Finder nearly useless for finding, so in the past I have in the past purchased a license to Path Finder, a Finder replacement/supplement app. There are other such apps as well.
Another option is using command-line tools in Terminal.app. For example, this article shows the use of the find command. See also this Question on SuperUser Stack Exchange, How do I find a file by filename in Mac OSX terminal?.
You can enter "kind: pdf" or "kind: text" to limit search results more in the search bar. I'm not sure what happens if it is a multi file name extension like .tar.gz.
