歩い isn't really a word, it's the te-form of 歩く with the て dropped (that's a typo, I hope).
歩く is the verb "to walk" - the action of putting one foot in front of the other.
散歩 is a noun or alternatively a する verb, it has a nuance of relaxation, not having a particular destination you need to get to, etc. If you go for a walk in the park or take the dog out for a walk, that's 散歩.