Differences between OWP and OWF and their IND-CPA security I am learning about one way permutations and one way functions and am not sure of the differences if there are any.

Also in the random oracle model are they both IND-CPA secure?
A one-way permutation is just a one-way function in which the function is a permutation (id est, a bijective function). Every OWP is a OWF, the converse is not true.

IND-CPA security is a security notion specifically related to encryption schemes. OWF and OWP are not encryption schemes, hence they cannot be said "IND-CPA secure"; however, one can construct an IND-CPA symmetric encryption scheme from any OWF, or OWP. (for asymmetric encryption schemes, stronger primitives are needed).