The service will operate on the selected text, files, or URL in any program that supports Mac OS X services. This should be just about all of them these days. You can tell by whether the command is visible in the Services menu.
The capture key works in applications that EagleFiler specifically supports. This requires that the application support AppleScript and that a capture script has been written. The full list is here, and you can also see in the Drop Pad whether the current application works with capture.
The capture key is generally for importing “bigger” items. For example, to import the selected text from Mail or Safari you would use the service. Pressing the capture key would import the selected messages or the current Web page (no matter what’s selected).
The capture key is also useful for importing items from other applications without having to first export them. EagleFiler will pull out as much metadata (flags, tags, notes, dates, labels, etc.) as possible and preserve them, whereas in most cases this information would be lost if you used the application’s own export feature.