According to Oxford Advanced Learner's Dictionary, camaraderie means:
I thought camaraderie and friendship were nearly synonyms. However I came across them both in a sentence 
What is the difference between them? Is it formal if I use the word camaraderie in speaking?
I would say that camaraderie, as either spoken or written, is used of situations having some of the following characteristics,
Brought about by shared dangers or hardships
Being on the same side in the struggle against something threatening
Having shared values and objectives
A wish to acknowledge and encourage each other
A sense that some misfortune can be overcome by shared willpower.
Friendship is usually quieter, but could develop from camaraderie, as when two old combatants enjoy reminiscing in old age. But in general, friendship lacks the tension and the urgency of camaraderie.
I would say comradery is more sophisticated (or philosophically beautiful) than friendship and used more often in professional environments. Its also more of mental trust we have with our team members or colleagues. Friendship is more of social thing and friends can be separated by a long distance and time of not communicating with each other, but still they are friends. You can also say that the mother of friendship is comradery , the time we have spent together because of same college, school, class or job, project and our comradery resulted in a long term friendship, that we still have even though we have not talked to each other from years.
As a native English speaker, I would say that "camaraderie" refers to the emotions caused by friendships, while "friendships" refers to the relationships themselves - this is supported by the dictionary definition of camaraderie that you provided. So, if someone says they miss the camaraderie and the friendships, they're saying that they miss both the relationships as well as the emotions that those relationships created.
