Hi Mehrdad, There’s some difference in meaning between them, and also a difference in their typical context. They both have to do with over-confidence and egos that are too large, but cocky has more of an association with boasting, where conceited is usually quieter and more internal. Cocky is the term used more for (especially young) men. Conceited is mostly associated with women of different ages.

Both words describe how a person feels about themselves. A conceited person is excessively proud and vain. A cocky person is a conceited person who is very loud and boastful about how they feel. They want everyone to know it.