Little-d distributed systems: the accidental sort. You built a program, it ran on one server. Then you added a database, some caches, perhaps a job worker somewhere. Whoops, you made a distributed system! Almost everything works this way now.
Big-D distributed systems: you read the Dynamo paper, maybe some Lamport papers too, and you set out to build on the principles set forth by those who have researched the topic. This is mostly open source distributed databases, but other systems surely fall under this category.
Ph.D distributed systems: you went to a top CS school, you ended up working with a distributed systems professor, and you wrote a system. You then graduated, ended up at Google, Facebook, Amazon, etc. and ended up writing more distributed systems, on a team of even more Ph.D’s.
If you’re building a little-d distributed system, study the patterns in the Big-D distributed systems. If you’re building a Big-D distributed, study what the Ph. D guys are writing. If you’re a Ph. D distributed system guy, please, write in clear and concise language! No one knows or cares what all the little greek symbols are, they just want to know what works, what doesn’t work, and why.