I've read an article that mentioned something like neutral Karma, and it seems it is no more/less than no Karma. Does anything differentiate neutral Karma from no Karma?
In Tibetan Buddhism, there is neutral, or indeterminate, action (=karma) which is defined as action the effects of which will never ripen as experience -- such as e.g. unintentional action that has no observable effect.
Does anything differentiate such neutral Karma from no Karma?
First, we need to remember that "karma" means "action", not its unmanifested effect. Traditionally, experienced effect of an action is compared with "fruit". We say that action "ripens" or "fruits". The action whose results are yet to be experienced is called "unripened" action, or "action that is yet to fruit" etc. When we substitute "action" for the special term "karma", we get "karma that is yet to fruit". To use the word "karma" to refer to its unmanifested effect is technically incorrect.
To clarify, in the phrase "neutral karma" -- the word "karma" should be understood in its correct sense of "action".
Second, when we talk about "fruit" of action in context of Buddhism, we mean an experience of the effects of the action. We should be very careful here and avoid any kind of materialistic bias. We are not talking about so-called "objective" effects of an action, but only how these effects are to ripen as (subjective) experience. So even though action has an effect, if this effect is not to be experienced at all, the concept of good or bad "fruit" does not apply. When this is the case, we don't speak of "good karma" or "bad karma", even though karma (action!) has clearly been performed.
Armed with the above we can now understand, that when we say "neutral", or indeterminate, karma -- we mean an action that is never to ripen as experience. This means such action that neither has "external" effects that will ever ripen as experience, nor shapes the mind of the performer in such way that will ever ripen as experience.
To tie this back to your question, your intuition was correct, indeterminate or neutral action is very similar to NO action, except technically an action has been performed, so, objectively speaking, there must be some kind of effect, however microscopic. It is just that this effect is never to fruit as someone's experience.
To the best of my knowledge, there is no such thing as neutral karma. As you rightly surmise, it would be the same as non-karma. This is because karma in Buddhism refers to ethical intention, not the act itself:
cetanāhaṃ, bhikkhave, kammaṃ vadāmi. cetayitvā kammaṃ karoti — kāyena vācāya manasā.
It is intention, bhikkhus, that I say is karma. Having intended, one performs karma, by body, speech, or mind.
In Theravada Buddhism, consciousness without ethical intention is called "avyakata" or "indeterminate", and is "karmically neutral", which is not the same as being "neutral karma", a term that doesn't make much sense from a Buddhist point of view.
lit. 'indeterminate' - i.e. neither determined as karmically 'wholesome' nor as 'unwholesome' - are the karmically neutral, i.e. amoral, states of consciousness and mental factors.
They are either mere karma-results (vipāka, q.v.), as e.g. all the sense perceptions and the mental factors associated therewith, or they are karmically independent functions (kiriya-citta, q.v.), i.e. neither karmic nor karma-resultant.
In Abhidhamma there are 3 kinds of kamma. To my limited understanding it goes like: mundane unwholesome karma, mundane wholesome karma, and supramundane wholesome karma. It's supramundane wholesome karma because it is the karma of arahants. It's also called "neutral" because it has no karmic potency unlike mundane wholesome karma. I think another word for "neutral" would also be "functional".