A face grain to face grain joint will usually fail at least partially along the growth rings in the board(s) rather than at the glue joint, yes. But an end grain to end grain joint (which are rarely made for practical reasons) will typically fail at the glue joint.

Wood is kind of a composite material; it's cellulose fibers bound together with a polymer called lignin. PVA wood glue is stronger than lignin but not as strong as the cellulose fibers, so a broken face-to-face joint will break along the weakest, the lignin.

If you edge glue a panel together for say a table top, gluing boards edge-to-edge, that board will be at least as strong as if it was one wide board; it will take at least as much force as a single board to break.

But, if you glue two long boards end to end, it won't be as strong as a single continuous board of the same overall length. It will fail at and along the glue joint, maybe pulling a couple splinters out of one board. Which is why we basically never do that; if a board has to be spliced it's common to add a doubler so there are fibers crossing the joint line.

But yes PVA glue like Titebond is amazingly good at bonding wood.