What that generally means is that the set was designed to fit the (insert kit here) kit. In this case, the Italeri kit. It will fit the Italeri kit perfectly but may not fit other kits without a little persuading. Depending on which kit you choose, persuading it to fit it may be simplicity in itself or it may be a months-long saga of re-engineering both the kit and the aftermarket parts.
If you like a challenge you should not let this stop you. If you like simplicity, plan on using the kit for which the aftermarket set was designed.
The difference between model companies is not huge, but there are definite differences in the models they've all issued. Those depend greatly upon when the model was first produced (Revell kits, for example, can often date from the 1950s and 60s). There are often more variations between models produced by the same company than there are between two models of the same aircraft produced by different companies. That being said, plan on there being differences. Two (or more) different groups of pattern makers working in different countries and using different references will result in each model, while recognisably being the desired subject, having slightly different proportions and construction choices.
References are critical. Back in the bad old days of the Cold War, there was next to no information coming out of Soviet bloc countries about their latest and greatest aircraft, so the model companies had to rely on guesswork and poor quality photos. This resulted in the Airfix MiG-21 being very different from the Hasegawa MiG-21, for example.
