Questions about example sentences with, and the definition and usage of "Yoghurt"

A: They’re the same thing! Some places uses yoghurt while others use yogurt.

A: The first is more indirect. The second is slightly stronger. Otherwise the same.

A: They are different spellings of the same word. I think 'yogurt' is more common in the US and 'yoghurt' is more common in the UK. Yoghourt is rarely used.

A: The key is in the preposition. If we substitute yoghurt FOR cream, then we using yoghurt as a replacement for the cream. In other words, you can use yoghurt instead of cream - same as: you can use yoghurt to replace the cream. Conversely, your second example means the opposite: you can use cream instead of yoghurt.

A: but I think it is yogur in Spanish isn't it?

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A: × I planed to eat yoghurt for breakfast, but it was out of stock.
✓ I planned to buy yoghurt for breakfast, but it was out of stock.

Your sentence isn't incorrect. But it is weird to say that you planned to eat the breakfast and then say that it was out of stock.

It could also be
"I planned to eat yoghurt for breakfast, but the shop was out of stock."

It's more natural to reference the act of having to go to a shop.

If you mean to say that there was no yoghurt at home, then you can say,
"I planned to eat yoghurt for breakfast, but I ran out/there was none left."

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A: definitely better

A: kinda sounds like you are saying it with an asian accent haha.