Htydjtk

I thought "on its way" and "in its way" were pretty much equivalent in English and meant pretty much the same thing except in very rare cases. Am I wrong? How do you know which one you should use?

They are not equivalent. "On the way" means that the location or object is along, adjacent to, or near some route.

If we're going to John's house, can we stop by the store to pick up some snacks? It's on the way.

"In the way" means that the location or object is directly in the path or blocking that route.

You used to be able to see the ocean from that hotel, but recently they built a larger hotel that's in the way.

Another way to think about it is that something on the way is convenient, while something in the way is an obstruction. It's possible to have both in the same sentence:

On the way to Lauren's house out in the country, we were delayed by a herd of cows that were in the way.

Moreover, "on the way" only really makes sense when talking about something related to people, or other entities that have the ability for conscious choice, even if it's only to specify some point of interest.

The restaurant is on the way to our hotel, if you want to stop for a quick bite.

"Fire" would not qualify, as it is mindless. A fire would not stop at a corner store to pick up a bag of chips (a.k.a. crisps) on its way to burn a town. Instead it might burn down the store, if it was in the way.

I can't think of any case where you can freely substitute one for the other without changing the nuance.

They can mean similar things in many cases, but they are definitely not always the same. For instance, 'in' can mean 'inside [of]' while 'on' can mean 'on top [of]'. There are too many use cases to explain. You pretty much have to know them all in a case by case sort of way.

In your example, they mean different things, but the effect could be similar.

'The fire consumed everything in its way' means that the fire burned everything that was blocking its path.

On the other hand, 'The fire consumed everything on its way' literally could mean 'everything' (rather than just everything in its path). However, people would probably understand your intent.

Doing something on the way doesn't have to mean that the direct object is nearby: e.g. 'I called my friend on my way to the dentist.' Your friend could be in another country.

A fire could destroy things far away on its way, too. For instance, the destruction of a bomb factory in its path could blow up the whole town on its way. I think it would be reasonable to say the fire destroyed the town, but people could argue that. Or a fire might cause a beam to fall that triggers a switch that makes a rocket launch that causes who knows what else to happen. Anything the fire could do during its journey could be done on its way.

However, when it comes to humans, there is sometimes a context that implies convenience (but that context doesn't always exist). For instance, "Since you're already going to Chicago, will you pick up some stuff for me on the way?" That's about convenience, while, "I called my mother on the way" isn't necessarily.

It's pretty common for 'in' and 'on' to mean different things.