Well “Mapnik” hasn’t really been a tile layer since Barack Obama’s first term as president 
It dates from when there were two tile layers, one using some software called “Mapnik” and dating from before 2012. In 2012 the “Standard” style on osm.org changed to use “OSM Carto” stylesheets that are much easier to edit - compare this with this.
I’ve changed the wiki page to reflect what actually happens - in a new browser page or new empty tab you’ll get the “Standard” style, but otherwise you’ll get whatever style you were last looking at.