Why might the cells of two different organs respond differently tp cyclic AMP activation?

Cells have different receptors on the surfaces that respond to different molecules that bind to respective receptors. Additionally, two cells types with the same receptor for the same molecule can respond differently due to differences in the activation of secondary messenger chains. Most of the downstream signals of cAMP are propagated by cAMP-dependent protein kinase A (PKA) which also varies in different cell types of different tissues.