Nearly and almost

[Legionofboom]

Are the words 'nearly' and 'almost' completely interchangeable or are they like 'less' and 'fewer' to be used in different circumstances? I have been asked what the difference is by a non-native English speaker and I have no idea.

In the dictionary they are both defined as the other. Is there a difference?

(Sorry for any errors in this post. I live abroad and I am often asked questions about English grammar and I know I am really not the person to ask )

Do you know you can Google questions like this?

Anyway, I would have said that they are pretty synonymous, but this link does tease out some uses where they are not interchangeable, eg "I almost never raise my voice" - can't use "nearly".
dictionary.cambridge.org/grammar/british-grammar/almost-or-nearly

That link includes these examples:

1. That guy is almost impossible.
2. The chicken is still nearly frozen. I thought youd taken it out of the freezer.

They say you could use nearly in 1, but that sounds slightly odd to my ear.

For 2, I'd find "almost" more natural. Saying "nearly" to me conveys we are heading towards that state, so I would only say "nearly frozen" if I'd put it into the freezer and it was heading towards a frozen state.

But maybe those reactions are just me?

Thanks.