Even if default posts are stored in same table but they have different behavior and different characteristics.
CPT has post type archive but default post type archived is called as blog and the taxonomy filter is called as tag/category archive.
You can access the category/tag archive using
For categories:
/?cat={category_id} //e.g. ?/cat=5
For tags:
/?tag={tag_slug} //e.g. ?/tag=my_tag_slug
If you are willing to use pre_get_posts you can customize this in the way you want (That is what I love in WordPress <3) else stick with default way.
Another note: I recommend to leave the default posts for blog never use them for building something custom with those types instead use CPT as many as you want to expend your site from blog to CMS 🙂