Exclude a category tag from Blog page and show it in the menu section only

I want to have two separate blogs in my website. Blogs and articles. All post with the blog tag I don’t want them to appear in the article section. They should only appear in the Blog section.

Here is what I have done.

I did some php coding and I was able to remove all post with the blog tag. So now my article page only shows articles.

I went to menu and selected the Blog tag to appear in the menu. It shows all my post with the blog tag which is great. The problem is that I have the pagetitle: Category id: Blog.

I want to remove this.

Any suggestion?

Here is the link: https://www.matureaging.com/category/blog/