The real meaning of the word 'important'

The word 'important' can be confusing in English. It has many meanings and is not quite the same as in French. It means 'high priority', 'of great significance' or 'matters a lot'. For example:

Filling in my tax form before 30 June is important. If I miss the deadline, I will be in big trouble. (=My tax form is high priority, it matters a lot).

She thinks voting in the elections is important. (She thinks voting is of great significance, it matters a lot).

However, important does not mean 'physically large'.

So if someone says:

"Manchester is an important city", they are saying that it is of great significance, not that it is physically large. If they want to also say that it is large, they would need to say something like:

"Manchester is a big and important city".

Here's another example. If someone says:

"I have a really important task to do", they are saying that it is high priority, not that it is physically large. If they want to also say that it is large, they would need to say something like:

"I have a big, important task to do".

Does this make sense? Any questions? Are there any other words in English that you find confusing? If so, please write in the comments below.