[Grammar] It has rained since morning.

[5jj]

There is not a clear difference.

I used to explain the difference by giving my own experience of living in Prague. I said that I realised that Prague was my permanent home when I noticed that I was saying to friends in England I live in Prague/I've lived in Prague for five years rather than I'm living in Prague/I've been living in Prague for three years.

There was a degree of truth in that, but I'm fairly sure that I sometimes used the non-progressive form back in the early days when I knew (or thought I knew) that Prague was not my permanent home (I left Czechia three times before I realised that I was going to settle here permanently.) I also wrote recently to an old school friend I haven't been in touch with for years I am living in Czechia now; I've been living here for twenty years now. That was after I had been granted Czech citizenship and had bought a flat here. There is not the slightest doubt that I am permanently resident here.

The progressive aspect always suggests in some way or other the limited duration of a situation. When the verb denotes an action that is in itself of very limited duration, the progressive aspect may indicate an repeated action: My allergy was bad today I was sneezing all morning.
When the verb denotes a situation than is itself of a longer duration, then the suggestion is sometimes more on the limitedness of the duration. This explains the difference I noted in the first paragraph.

The limited duration emphasis explains why it is often used for a situation in progress at a particular point/period in time: I am writing a response to englishhobby's question (at this very moment); half an hour ago I was discussing our holiday plans with my wife. It is this that explains the use of the aspect in I am living in Czechia now; I've been living here for twenty years now. My focus was on my situation at the moment of writing rather than simply on my residence.

 

[jutfrank]

What I meant was that I wish I could feel the difference (both in use and meaning) between those two particular sentences with the verb 'to live' ('I've lived here all my life' and 'I've been living here all my life') as they are different from the common examples with the verb 'to have' like "I've had this book' or with the verb 'to know' (you cannot say 'I have been having this book' or 'I have been knowing this person', they are just not grammatical, while 'I have been living here all my life' is quite grammatical).

That's because in your examples, have and know can only be purely stative whereas live can be both purely stative and active. When used with a continuous aspect, live is not purely stative. I think this is what's confusing you.

Even if no student will ever ask me about it, for me personally understanding of this particular difference is important.
So, I would be grateful if someone gave me some contexts in which the difference between those two particular sentences with the verb 'to live' ('I've lived here all my life...' and 'I've been living here all my life'), especially the extra meaning given by the continuous aspect, would be clearly seen.

You have to think about the meaning of the verb live as used in context. In a continuous aspect, it isn't purely stative. In fact, it's better thought of as more essentially active. The verb work is similar, in a sentence like I've been working here for a year.

It might help you to think of the difference like this:

I've worked here for two years.

This expresses a pure state. It means something like The proposition I work here (a pure state) has been true for two years. The sentence I work here is a pure state because it expresses a simple relation between me and my place of work. There's no sense of activity in essence..

I've been working here for two years.

In essence, this sentence expresses an action. It means that I've been active here for two years. This action is ongoing.

 

[5jj]

When used with a continuous aspect, live is not purely stative. I think this is what's confusing you.

I can't see the difference between I have lived here for two years and I have been living here for two years as a stative/active difference.

 

[jutfrank]

I can't see the difference between I have lived here for two years and I have been living here for two years as a stative/active difference.

Can you see the difference with work substituted for live?

 

[5jj]

No.