To answer the main part of your question: Yes, there do exist such systems. They're called visual binaries. We generally need a telescope to tell them apart. Most binary systems look like a single star when viewed with only the naked eye; many cannot be resolved without the aid of a telescope. But visual binaries can.
also is there any binary stars doesn't linked together by gravity
No, there aren't. You were right when you said that the definition of a binary system is basically two stars orbiting a common center of mass. If the stars don't orbit each other, they aren't a binary system.
By the way, check out Proxima Centauri, the nearest star to the Sun. It's one of the three stars in the triple-star Alpha Centauri system. The reason I mention it is that even though it's seemed for years like it was gravitationally bound to the system, that idea is now under debate.
Let me address something that Mitch pointed out. The classification of star systems as "visual binaries" is based solely on our ability to observe them. If we had better telescope, this class could change. An analogy might be our naming certain wavelengths of light "visible". They only depend on our perceptions, not some objective characteristic that all observers in the universe could agree on.
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