This is one of the more confusing things that Tridion does. Once you know how it works it's fine, but you have to know.
So... when you ask Tridion to publish something for you, it figures out what should get published. This is called resolving. The result of resolving can be seen if you click the "see items to publish" button in the publish dialog.
Anyway - if the list of "things to publish" determined by resolving is empty, then publishing will succeed very easily. Tridion will tell you straight away - Yes, I have published all the (zero) things I should have, and none of them failed, so that represents success.
Why might some things not resolve? The first thing I'd look for in your situation is whether the item is already published. The publish dialog has a check-box for this. Something like "Only publish items that are already published". This (quite correctly) is the default.
This is where one publication target can be different to another. If you're publishing to STAGING, and the items in question have never been published there before, unless you specify "items that aren't already published" (or whatever the wording is), the currently not-published items will not feature in the resolving results, so you'll end up publishing nothing.... which will succeed very quickly