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I realise the comparison is not ideal, but what is actually happening?
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That's actually a pretty good description.
Going downhill in an airplane is a lot like going downhill in a car; often the power is reduced and the tendency is for the aircraft to want to speed up. Going uphiill, just the opposite. The tendency is for the airplane to slow, and more power is required to get up the hill.
When landing, we don't necessarily want to land fast. We use flaps of varying types on the front and back of the wing to create extra lift and drag, and this enables a slower approach to landing. This means a shorter landing distance, a safer landing, cooler brakes, etc.
When the aircraft is descending to land at a given speed and drag is incresed by lowering flaps and landing gear, power will have to be increased to maintain that speed. You can think of flaps and gear as applying the brakes on a bicycle or car, as it goes down hill.
In order for an airplane to fly slower and slower, it needs more and more power. This becomes a little more complicated, but at slower speeds, the wing must fly at a greater angle, and at a greater angle, there's more drag (and lift). As the angle the slipstream meets the wing increases, drag increases faster than lift, when landing...and more and more power is necessary to progressively fly slower and slower.
So long as we keep going downhill at a given airspeed, not a problem. However, if we increase the flap setting and hold that airspeed, then a power change is in order. Also, if the aircraft dips a little low on the glidepath as it approaches to land, then increasing power becomes necessary. The heavier the airplane and the more drag it's got out (gear and flaps, again),the more power is required to get it back on the glidepath, without losing the necessary airspeed.
Lugging down final in third gear is a very good analogy, as more and more power is carried to do seemingly less work. The power certainly isn't producing great speed, so what it's doing is overcoming forces you can't really see or feel while sitting in the airplane, and chief among those is the induced drag of the high angle of attack (angle between theslipstream and wing) experienced by the airplane. As you can't see this change or really feel it, what you do feel is an increase in power and a slow airplane, with more noise, and you're quite right...it feels like chugging down the road slowlyin third gear before the car is quite ready to go there.