How does Snapchat store its data?
All good, future-proofed databases are normalised to some extent. Normalisation is described by Louis Davidson ~ Pro SQL Server 2008 Relational Database Design and Implementation as


  The process of normalization is really
  quite straightforward: take entities that are complex and extract
  simpler entities from them. The process continues until every table in
  the database represents one thing and every column describes that
  thing.


So based on your example I would imagine that the Snap Chat database (assuming that we are talking about OLTP model and not using NOSQL / BIGData) would have multiple entities, with each entity containing relevant data and be related to other entities via the appropriate relationship i.e. 1..Many, Many to Many etc. For example, a person entity might contain UserName and Password and be related to a loginToSite entity via a 1..M relationship. I suggest a 1..M relationship because one person can log in to the site multiple times but each login to site record will only be related to one user. If all attributes were stored in the a single entity then in this example the UserName and Password information would be duplicated per Login record and break the rules of normalisation. This would also lead to a database usability nightmare!!

Depending on business rules, and these would be questions you would have to ask snap chat. One user record might be related to one or many photo records or maybe one user can be related to one or many photo records and one photo record can be related to one or many user records. In this case, there would be a many to many relationship. 

When thinking about database design it's important to first work out the conceptual design by talking with end users, reviewing reports / spread-sheets (anything containing data used by the end user) and generating an ERD. Then once the relationships have been agreed, all data to be stored captured and the ERD modelled you can move onto the physical side of things and work on performance, choosing data types, deciding on indexes etc...