If for “current page” you mean a WordPress standard page (i.e. a page created in the menu Pages > Add new), you cannot grab pages related to the current page because they have not any taxonomy.
If you mean a blog post page, in this case posts can have taxonomies. Currently you can grab posts related to the current post using the category of the current post (I explained it here). There is a dedicated section in the widget admin for this.
In this section, the %s
placeholder is used to display, in the widget title, the category where the posts are retrieved from. It’s used only for this scope.
Please, let me know if I am correctly understanding your needs.