I am not sure what you mean by “real OS”.
That notwithstanding:
Ubuntu Mate desktop installed from the Ubuntu Mate ISO consists of the Ubuntu underlying base system plus a significantly tweaked Mate desktop over the top of it. Those significant tweaks are what constitute the “Ubuntu Mate” desktop, as opposed to merely the “Mate” desktop.
Ubuntu Mate desktop installed manually over the top of an existing Ubuntu base+desktop system includes all of the above. That is to say, it includes the “Ubuntu Mate” desktop and not merely the standard “Mate” desktop. But, it also includes the Ubuntu standard desktop which, as far as I am aware, is currently Gnome 3.
So, the next question is; are there any differences of performance between the two?
The answer to the above question comes in two parts.
The first part concerns “redundancy”. That is to say, there will be likely a number of Ubuntu Mate applications that will be replicated in the Gnome 3 desktop (in the scenario where you manually install Ubuntu Mate desktop over an existing Ubuntu standard installation) and, although you may be logged in on an Ubuntu Mate desktop session, these Gnome 3 apps will still appear in your menu. In itself, this should not affect performance and is only an aesthetic issue and/or a storage issue if your hard drive is particularly small.
The second part concerns “performance”, in real time, of the system. I can only answer this question from personal experience since I lack the technical expertise to give a categorical technical answer. In my personal experience, I have found that when I have installed one desktop over another, performance takes a small hit. But, often, it is sufficiently small as to be irrelevant. Finally, very occasionally, other little niggles are introduced. These are often a bit random and may be something like scrollbars or other themeing items not quite working right. But, I have found they can usually be rectified.
So, in short, the answer to the question of whether there is any important difference between the two installations is no… more or less.