Simply put:

I have the "K2 Content module" module menu assigned to a page named "blog". When I click on a title of an article it shows a page with the same "K2 Content module" content AND the full article on the same page after each other.

Observations:

I am using another instance of the "K2 Content module" for my front page. Which works as wanted when I click on the title, showing just the whole article itself.

A difference I can see is that the working frontpage module takes me to the address:

vww.mywebsite.com/component/k2/item/1-the-blog-post-i-want-to-see

When the problematic module assigned to the "blog" page takes me to:

vww.mywebsite.com/blog/item/1-the-blog-post-i-want-to-see

So what is the missing clue here? Thanks!! B)

Found the answer! This was a Joomla issue:

[SOLVED] Assign module content: absolute path not relative

One solution:

Not to assign any menu items for the module, simply enable the module, then edit the menu item to be that module content. Thus that content will only show up in that menu items absolute path.

yippie!