An idiomatic phrase and a literal phrase differ primarily in their meanings and usage. An idiomatic phrase conveys a meaning that is not deducible from the individual words it contains; rather, it has a figurative or metaphorical meaning that is understood within a specific cultural or linguistic context. For example, "kick the bucket" is an idiom that means to die, and its literal interpretation doesn't convey this meaning.
On the other hand, a literal phrase communicates its meaning directly based on the definitions of the individual words used. For instance, "kick the bucket" taken literally would mean to physically strike a bucket with one’s foot, which is entirely different from its idiomatic meaning.
In summary, the relationship can be described as follows: idiomatic phrases have figurative meanings that may differ from the literal meanings of their components, while literal phrases have meanings that correspond directly to the definitions of the words used.