Intrinsic and extrinsic motivation are often misunderstood. I was only able to fully understand it after I came across the different Regulatory Styles matched up with Intrinsic and Extrinsic motivation.

Motivation	Regulation	example: "I exercise because...
extrinsic	external	...I get paid for it
	introjected	...otherwise I'd feel ashamed
	identified	...it is important for my body
	integrated	...it reflects who I am and what I believe
intrinsic	intrinsic	...I enjoy the act of recycling

• Not when you think it's important.
• Not when you yourself freely choose it because you value the result.
• Not when you force yourself to do it, even though you don't want to

Extrinsic motivation is then any time you're motivated, but it's not intrinsic.

There is also Amotivation, which is when you're not motivated at all. So this is when you have neither intrinsic nor extrinsic motivation.

Why is this so often confused? Probably because intrinsic and extrinsic motivation sound a bit like internal and external motivation. And when you need to guess the then unknown term from the context, it's kinda good enough to translate it to the easy to understand internal/external terms. They are different though:

What about when I force myself to start something, but once doing it I kinda enjoy it?

It kinda sounds like 'the act of starting' is extrinsically motivated but 'the act of doing' is intrinsically motivated.

Why is this model useful?

Things that are intrinsically motivating, give me energy when doing them.

Extrinsically motivating things, don't give me (as much) energy.

But farther away from intrinsic motivation, I get less energy / it costs more energy.

In both cases I excluded the reflection/pat-on-the-shoulder stage, which can also create energy.

(src: Book: Understanding Motivation and Emotion 4th edition)