Photo Chemistry generally referes to the physical chemistry going on in the crystal and at the crystal-light interface. It is generally inorganic chemistry, but not always. George Byrd (of Princeton?) was one of the most prominent researchers in this. There are some physical chemistry texts on this.
Photographic Chemistry usually referes to the chemistry of processing. Haist, Henn and Lee are examples of B&W R&D here. Mees and James and Haist are good texts here.
Emulsion Chemistry or Engineering usually refers to making or designing emulsions. No textbooks worth anything. Many internal EK texts.
Photo Engineering usually refers to overall system design or someone who has had experience in all of the above. No textbooks worth anything. Many internal EK texts.
Coating Engineering is a side topic that refers to engineers who design coating equipment or design specs for making coatings of products. Many internal EK texts.
PE