You can try to ask LaunchServices for the app's location, given its bundle identifier with the LSFindApplicationForInfo call:
CFURLRef urlRef = NULL;
LSFindApplicationForInfo(kLSUnknownCreator, (CFStringRef)@"com.example.some-app", NULL, NULL, &urlRef);
NSLog(@"URL: %@", (__bridge id)urlRef);
This assumes that the bundle identifier is the same between the two variants you mention. If it's really just the name that is the same, you could query by name instead:
CFURLRef urlRef = NULL;
LSFindApplicationForInfo(kLSUnknownCreator, NULL, (CFStringRef)@"Test App.app", NULL, &urlRef);
NSLog(@"URL: %@", (__bridge id)urlRef);