The NC6 is the standard microgenerator notification your installer submits to ESB Networks for a domestic solar install — it registers you as a microgenerator (which you need for export payments) and covers connections up to the normal domestic limit (typically 6 kW export on single phase). For the great majority of homes, NC6 is all that's involved and you don't need to think beyond making sure your installer actually files it, ideally well ahead of the install date.
NC7 comes into play when you want a larger connection than the standard microgen allowance — for example a big array with a higher inverter/export rating, or a substantial battery system where you'd otherwise be export-limited. It's a more involved application to ESB Networks and can take longer. A useful real-world trick that comes up: fitting enough battery storage to soak up midday peaks lets a modest inverter avoid clipping, which can keep you inside the standard NC6 envelope and save you the NC7 process entirely — storage as an alternative to a bigger grid connection.
If you're a heavy user planning a large system (high kWp, big battery, three-phase or an upgraded MIC/main fuse), raise NC6-versus-NC7 with your installer early, because the connection paperwork and any capacity upgrade can drive your timeline more than the install itself. For a standard domestic 4–6 kWp system, this won't apply — it's NC6, your installer handles it, and the main thing is just confirming it's been submitted.