- weather is mostly about complex local interactions between air pressure / surface temperature / air flow (convection) / humidity etc. these are described by differential equations with very chaotic behaviour (small changes in inputs may have extreme effects on the outputs the further you run the model)
- climate is more about long-time effects of the energy input/output of the whole planetary surface and atmosphere. Mostly solar radiation (input) vs. black-body radiation (output). There are also some complex interactions and feedback cycles e.g. change of albedo (cloud cover), and changes of atmospheric composition (i.e. methane due to permafrost melting), but local weather patterns may cancel out when looking at the sum-total of surface thermal energy.