Difference between a table and a matrix

What is a difference between a "table" and a matrix?
One can use save command to write a matrix data to a file. Can one use the same save command to write a table to a file?

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They're similar but a table can contain different types of data, though all elements in a column must be the same. A matrix/array must have all elements the same, even in different columns, except for a cell array which can have different kinds of variables at an element no matter where it is (no requirement that all elements in a column of a cell array contain all the same type of variable like is the case with tables and matrices).
You can use writetable() to write a table to a file.

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save works perfectly for storing table objects in MAT files also.
How does the table differ from the cell array?
Tables are more memory efficient. Tables have a lot of nice functions for dealing with them, such as outerjoin, etc. Tables must have all variables in a single column be a single type, like string or double. With cell arrays, you can mix data types within a column, for example cell (3,4) could have a string but the next cell down at (3, 5) could contain an array or a structure or even another cell. See the FAQ for a good intuitive explanation: http://matlab.wikia.com/wiki/FAQ#What_is_a_cell_array.3F

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