Crashing is schedule compression, whereas smoothing is Resource Optimization. Both have no relation, except for that they are used in Schedule Management.
Crashing is adding more resources(or paying overtime) to speed up one or more activity. Ofcourse done on critical path. It may/surely will increase risk and cost.
Smoothing will use free/total float and will not change critical path, better make comparison of smoothing with leveling to understand it better. For eg you want to make your resource work for 20 hours only this week, you will adjust free/total float to reduce his hours to 20.