How do databases differ from MATLAB variables?

I'm used to working with data (sometimes large amounts of data) as matrices or cells in MATLAB. I'd like to make the switch to managing larger datasets through tools like SQLite.

So here is my question. How do I approach the conceptual switch from MATLAB variables (again multi-dimensional numerical matrices, as well as cells with text entries) to a database? For example, if I have a 4D matrix in MATLAB, is there a way to store that data directly as a table? Or would I have to do something like, say, make multiple labelled 2D tables? Is all data in a database stored in a table?

Is it right to think that the migration of data from MATLAB to a database would look like, more or less, a reorganization of the multidimensional MATLAB variables into a set of 2D tables?

Any experience with migrating data from a MATLAB environment to an sql-accessible database would be helpful.