Problem:

Checking whether each of the substrings in column A exist in the corresponding strings from the same row of column B.

Solution:

For case sensitive results: Use the ISNUMBER and FIND functions as shown in the following formula:
=ISNUMBER(FIND(A2,B2))
For case insensitive results: use the SEARCH and LEN functions as shown in the following formula:
=SEARCH(A2,B2&A2)<LEN(B2)