Data storage on servers and transfer if necessary. What are effective scenarios for solving the problem in 2018?

Question

Data storage

What are the modern methods of organizing the storage of website data? We are talking about downloadable media content - images, "gif", video (in case of storage on the project's own facilities), etc. How to effectively organize the migration of large volumes of such content in case of project migration to another hosting?
I've heard about Azure and S3, but haven't worked directly with them yet. If I understand correctly, then using such a storage as a solution to the problem is more appropriate than using your own (or rented) physical servers in data centers (we don’t take into account the issue from the point of view of small and medium-sized projects, giants like Facebook).

Answer 1

So, what's the problem? Copy files?
https://syncthing.net/

Answer 2

Well, use c3 if money allows