Dividing posts into 2 streams

You use categories – that’s why they were invented.
You exclude one or more categories from showing up on the front/home page. Search for a plugin like “category excluder”
The rest of the categories will be available only when you click on the category’s name and you are taken to that category’s archive page (aka category listing).
Done.

ACE is a great plugin and it is close, but not exactly.
It can address and configure what you want to display in different sections. You can configure what you can display in “Home” (main blog),
Archive and etc. But Archive is still archive and use different representation of data.
What I’m looking for is adding one more section with the same presentation structure as “Home” but with different address. ACE like configuration is excellent and would allow to separate content.

Maybe if you are able to explain this:

What I’m looking for is adding one more section with the same presentation structure as “Home” but with different address.

then somebody will understand what you want.

Sorry for being not clear.
I’m not very familiar with some of WP configuration options.
This may be fixable in template, but Archive is specific feature of the software. It is organised differently than main blog. What I’m looking for is main blog at front page(some posts should be excluded). ACE can do this.
Excluded posts (they can belong to excluded categories to have some sorting capabilities) are displayed at different location in blog format. By blog format I mean last post is displayed first, the same as at home page. Then, it should be some way to link to this second blog from menu.

Yeah, you should listen (instead of arguing) when I am saying this is exactly what I suggested.
An Archives Page and a category archive list are two [2] different things.
I am doing this for years… I knew what you wanted even after your first post. The problem is with your head – full of preconceptions and not open to read carefully the instructions.

If I was to exclude the WP Tutorials cat from my homepage at the links above, those posts would be visible ONLY when clicking on the category name, or from any kind of “menu” if I fancy to include that link into it.

So, what is the part that doesn’t do what you wanted?

OK, I think I got it. Disable “CAT_1” category for “Home”. Enable it (and everything else in Archive). Point to “CAT_1” category by setting a link to it (could be done in a couple of different ways). “CAT_1” is the second blog I was looking for. Thank you for opening my eyes.

??
And you can repeat the process with CAT_2 and CAT_3 etc… and then you have four “streams”.
Good luck!