First, I should point out that the first sentence is an abbreviated form of "testing is complete". This kind of abbreviated form is used in newspaper headlinese, notices and computer status displays.
As an adjective, complete means whole, so the following sentence means that all of the pieces of testing have been put together... probably not what you meant.
Testing is complete
As a verb, complete means finished, and I think that this is the meaning that you are looking for: the completed form is a past participle which, in this context, is used to form a passive voice sentence. You could use present simple to say
Testing is completed
but it is not what a native English speaker would say: they would be more likely to use present perfect
Testing has been completed
The difference is that present simple is used to talk about the way things are now, and present perfect is used about something that happened in the past (completion of the testing), that has an effect that lasts until the present time.