I don't own the beginner box, so I'm probably not all that qualified to answer this, but since the BB is meant as an introduction to the Pathfinder RPG, I would have to say that yes, in terms of rules, everything in the BB will be in the core rules (possibly expanded and altered to fit the needs of the full rules), plus lots, lots more.
What the core rules will not provide is pawns or an adventure.
Think of the BB as a stripped down version of the Core Rulebook. The CRB is about 575 pages, the two BB books combined are about 168 pages worth of material (with a higher art to text ratio).
The BB covers the basics of what you need to understand the framework, races, classes, class abilities, skills, feats, how combat works, etc etc. The Core Rulebook contains much more of all of that stuff plus additional systems (item crafting, magic item creation, combat maneuvers, and more). It is a platform product to get you to the Core Rulebook when you are ready for more.
Also, the beginner box has a lot of "tips for beginners" stuff which isn't as carefully spelled out in the Core Rulebook.
Is the content of the 2 separate players and GM books in the beginner box all contained in the core rule book?
No. As someone stated already, the monsters are not in the core rulebook. However, everything else is in the core rulebook.