When to recess a lag bolt in lumber, vs. using a lag screw?
Simply, a bolt is not relying on the holding strength of the threads in wood fiber.  It is a metal-to-metal sandwich that is holding boards together from both sides.  A bolt connection will normally be stronger than a lag screw, but that increased strength is often not needed, and access to both sides of the joint is not always possible.

If there is any question about the holding strength of the wood, a bolt is a better choice.  If the wood isn't very dense, or if it could get wet and soft (like an outdoor swingset), or if you need the maximum amount of strength then choose a bolt.

If the wood is solid and you don't have access to both sides, a lag screw is a proven solution.