I'm quite sure we could confuse you even further! Whilst immigration and customs work together in airports, they are separate functions with different reporting paths - UK Border Force (immigration) is the responsibility of the Home Office, whereas customs routes to His Majesty's Revenue and Customs (HMRC, think IRS).

For the vast majority of arrivals at LHR, yours included in both directions, the routine is this:

Stay airside

Follow signs to connections (this will be a walk/train if same terminal, bus if switching terminals)
Clear security
Go to lounge/gate

Go landside

Follow signs to arrivals
Clear immigration
Clear customs (walk-through, stops by customs officers are generally intelligence-led).
Go to departures level
Clear security
Go to lounge/gate

There are variations if arriving from or connecting to a Domestic flight or Common Travel Area, but these don't affect you.

Looking at this in isolation, most people would think it much quicker and simpler to take the airside connection option. In reality, those of us with e-gate access at immigration (you would get this if US passport holders) and priority security often find it quicker to go landside if within the same terminal (indeed sometimes even when changing terminals as well) because transfer security is frequently very busy.

Obviously when you start at LHR on your return it's much simpler - just security to airside.

On your last visit with your then young child, you would have encountered an immigration officer - more likely the question was designed to be humorous to make your child relax, but the immigration officer is also the first port-of-call for detecting kidnapping or child smuggling cases, as examples.