Difference between 散歩 and 歩い?

my book says they both mean 'walk'.
from what i gather it's kind of like the difference between "walking" and "going for a walk"?

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.

oh haha that was a typo my bad. but that explains it well, thank you! it had me confused :>