What is the difference between the uses of these two skills? What can be accomplished by a character with one of these skills but not the other? Is any there advantage in having both skills?

Presumably, to be a really good cryptographer, you'd need both. With the former you might have a theoretical if slightly abstract knowledge of ancient codes and their contextual use (in the real world for example you might know about Caesar's methods etc) whereas with the latter you would probably have a strong grounding in actual techniques like frequency analysis etc etc.

Scholastic Lore (Cryptology)

= Knowing about Cryptology. ex. The IG uses "X" numbers of standard encryptions that revolve around 'Y' process.

Trade (Cryptographer)

= You are a code breaker.

I would say both would be required to be efficient in breaking codes.

I would allow a Scholastic Lore (Cryptology) test to reduce the amount of time a Trade (Cryptographer) test would take to accomplish, a reduction of weeks to days, for instance.

It seems reasonable that Trade (Cryptographer) is the actual "doing" aspects of working with codes, but the description for Scholastic Lore (Cryptology) states, "This may be used to either create or decipher encryptions." This seems to overlap a great deal with, '"Used to create or decode ciphers, codes, and other puzzles."

Perhaps the "create" part is the difference. What if the Scholastic Lore only gives insight into working with known methods of encryption while the Trade allows for the creation of new ciphers and codes?

I'd assume it's a simple oversight on the designers' part, but assuming it isn't, I'd consider it the difference between Trade (Technomat) and all the different Lores that pertain to technology - the Trade allows you to perform solid, if a little unimaginative work while the Lore has you understand the underlying principles. Someone using the Lore to encrypt something would do it more slowly than someone with the Trade, but he might produce a result that's harder to break since it doesn't use the most widely-known ciphers. It's basically the difference between an academic and someone with job experience, but no real schooling.

given what both skills do they may overlap, the trade simple represents that you can break codes. the lore skill is your understaning of how a code is stuctured. in addition to these skills you have ciphers that are unique to an organization. you really have 3 skill areas that are based around cryptography.