We call a group of musicians an orchestra. In the same way, what would we call a group of programmers?
http://all-sorts.org/nouns/programmers has a few suggestions for a collective noun of programmers.
An array of programmers has the most votes at the time of writing with
a heap of programmers three votes behind.
A team of programmers.
I head a small team of programmers. How do I make them appreciate quality that every line of code they write is well thought of and every UI designed is simply beautiful?
I'm not aware of an -ography for programming. The term is simply 'programming' or 'software engineering.'
It's a Pride of Programmers. Why you might ask?
When programmers group up and get that first preemptive glimpse at the codebase they're about to absolutely annihilate, they become lions in that moment. From then on they're eternally hungry, they need meat (code meat that is). I'm talking function gazelles, variable antelopes, the whole nine yards. When they're in their natural habitat (terminals) they are lethal, mystical beasts to behold.
Can they run? Hell yeah! They can run programs...They're animals.
So I leave you with a Pride of Programmers
I agree that groups of programmers or software developers are usually referred to as teams, although that does have the nuance that they're working on the same project or for the same company.
If they're not related in that way, it'd just be a "group" of programmers. For example, you might encounter groups of programmers at a programming-related or technology-related convention.
Really, there's no fancy or unusual term for them. If you're being poetic you could make something up, like an "arrogance of programmers"!
As for your second question, there is no "graphy" word related to programming. A person who makes software programs, and is a programmer.
A person can study choreography, or cinematography, or they can study programming. If you're fancy, you can call "programming" "software development" instead, but "programming" fills the same niche that the other two words do for their industries.
A sub-type of programmer will sometimes have the word "architect" appended to their title or description. Others will have "engineer". Perhaps that's what you're going for? But titles are highly interchangeable in the industry now and there's not any formalized definition between programmer titles (programmer vs. developer vs. engineer vs. architect) that isn't tied to whatever a specific company's HR department decides.
Source: Worked in IT for 10 years. Met a lot of programmers!
a group of people with a shared characteristic
'a cohort of civil servants patiently drafting legislation'
a group or system of interconnected people or things
'a trade network'
a cohort of programmers; a network of programmers