You didn't say how it differs, or how you were adding it up, or what precisely you were looking at, so I'll have to answer in general terms.
There are certainly correlations. Some noise will correlate in frequency - it will end up translated into different sidebands by the cyclostationary nature of the circuit, and then translated into the output band - the root cause of two different noise contributors could be related though.
Similarly some noise sources are bias dependent (e.g. shot noise) and so there will be some correlation between the noise from different sources for that reason.
Noise separations is generally to tell you information about where the noise is coming from - but you wouldn't use it to compute the total noise yourself (the simulator will do that for you, as it's in possession of the full information).