Yes, it's not very clear there, I'll put up a photo guide at some point since even the LGW website is a bit unclear on this.

The following summary for North terminal:

Domestic plus Irish to International at North - if you arrive in the domestic area and arrive by airbridge, there is a flight connections route, a bit of a maze but all airside. There is an easy to miss but signposted left turn (most people will be going straight ahead to the exit), this will take you to someone who checks your boarding pass. I found it open late at night on a Saturday, much to my surprise, so I think it's always available. There is a further passageway, which then takes you to just to the right of the passport area for arriving international passengers. There is a security check, you then go upstairs and end up by the Premium Gatwick security exit by the Duty Free shop.

Domestic to domestic, international to domestic, bus domestic to anywhere: you must go via landside, so exit and reenter via main security or Premium Gatwick.

International to international: easy, all airside, just use the Flight Connection and security to the right of the UK Border (part of the Domestic path mentioned above).

North To South terminal: there is a bus service airside between North and South. You can use this for international connections only, Irish is not international in this context. This also feeds off the back area of the UK Border in North Terminal, so domestic bus passengers cannot get there and have to use the landside transit.

South to North:Airside bus which runs on demand. The passageway is on the final approach corridor to the UK Border, typically on the left hand side for most arriving passngers. Again it can't be used (or reached) by Domestic and Irish arriving passengers, or those connecting to North domestically. They all have to go landside.

[I'm praying they do something to improve domestic arrivals at South, the current set up involves buses and is not at all good, I can see trouble ahead!]