Career path highlights the path planned through your organisation - both laterally and vertically - for a high performing professional, to be progressively groomed to take on more and more senior roles.
Learning path is the corresponding sequence of Learning activities that this professional will need to undertake, to be able to face the challenges at each level in their career path and move to the next level.
In the language of gaming, think of the career path as the path the player takes through various levels until finally reaching the topmost - and most difficult - level of the game. The learning path consists of all the various weapons, tools and powers that the player needs to acquire at each level / set of levels, to move onto the next higher level / set of levels.
This is also where the 'Peter Principle' becomes relevant - that every individual rises in his/her career upto the level whereafter their incompetence becomes dangerous for the organisation, thus preventing any further promotion / growth. The idea of a Learning Path is to prevent / pre-empt the Peter Principle from becoming real.