The specific places they disagree require higher maths to appreciate - it is not that they cannot be phrased just using English but that it is too easy to misunderstand the normal-language version. That is why we use maths, and why we have jargon. Just try explaining Newton's Laws of motion to a five-year-old using only words they understand.
So what is your education level?
Bearing that in ind, I can give you a basic, in a nutshell, idea of where the conflicts arise.
There are four fundamental forces in classical mechanics ... these are: electromagnetic, strong nuclear, weak nuclear, and gravitational.
QM gives us Quantum Field Theory which gives us the Standard Model of Particle Physics ... this models the fundamental forces as interactions between particles, the forces themselves, the rules you may be used to from secondary school, are what happens on average over a very large number of these interactions. In this picture, the laws of physics are statistical - lots of randomness and things happening with no cause, though cause and effect do happen.
GR models gravity as a pseudoforce emerging from the curvature of space-time associated with the distribution of energy. Much like the centrifugal force is a pseudoforce arising from rotation. Mass happens to be a very high concentration of energy so it has a strong effect on the appearance of gravity. In this picture, forces could be described as a form of geometry - and the laws of physics are deterministic in the sense that cause and effect is an illusion created by our relationship with the dimension of time.
See how these two pictures are fundamentally at odds with each other?
This is by no means complete.
A more detailed answer would need extra information, like your education level and what you want the answer for.
Like: do I suggest MIT open courseware lectures? There is a very good series on how classical mechanics works, for example. But if your physics is at the junior secondary school level there is no point.
