In
UltraEdit I use UltraEdit projects and so the tagfile for the project is specified in the project settings and is stored in the project directory. I do not use the default tagfile which I have set to be created in the UltraEdit directory because I never use ctags for files without project except for tests to answer forum user questions. If you do not have a project with project files UltraEdit only runs ctags.exe with the current file as only source which is normally not really helpful.
UEStudio does not have the option to specify a project specific ctags tagfile in the project files dialog as UltraEdit. In UEStudio an additional tab for project settings is available were you can choose between the integrated UEStudio tag support or use UltraEdit method with ctags. See help of UEStudio about "Project Settings dialog" and "ClassViewer".
The Ctags support in UEStudio with the default tagfile is like in UltraEdit only for the current active file, when no UEStudio project is currently active.
Have you already run the ctag file creation? This is an extra menu point and you have to run the creation/update of the tagfile always manually. With a project tagfile you can also set it to automatically create/update it on project open.
The advantage of the integrated UEStudio tag support is that the tagfile is automatically updated during editing and you can use the class viewer. I suggest first to try the integrated UEStudio tag support with projects which really works good for C/C++.
If you do not want the integrated UEStudio tag support and choose ctags, it is not important where the ctags tagfile is stored and which name it has. You only should have write access to the directory where the tagfile will be created.
For help about the parameters for ctags see in help of UEStudio the topic "Ctags support". The help for Ctags itself with a detailed description of possible parameters can be found at
http://ctags.sourceforge.net/ in the documentation files in the archive file ec554w32.zip.