걷다
this refers to the literal act of walking
걸어가다 is to go somewhere by foot.
걸어오다 is to come somewhere by foot.
-> both are basically “to walk somewhere” and the difference is in whether you would use 가다 or 오다 for your sentence
산책하다
this is used for leisure activity and exercise. it is better defined as “to stroll” so if you are walking for fun or exercise, you can use this.
walking in the park? taking your dog for a walk? 산책하다
you 걸어가다 to the park and once there you 산책하다 around the park^^ during all of this you are 걷다 ~
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~ Shelbi
Satyanghae Korean 