The four basic reaction types can be outlined as follows:
A + B -> AB
AB -> A + B
Note that the synthesis and decomposition reactions are exact opposites of one another; if you run either of them in reverse, you get the other type of reaction.
Single Displacement Reaction:
AB + C -> AC + B
Double Displacement Reaction (also known as a Metathetical Reaction):
AB + CD -> AC + BD
The reaction you are asking about is a single displacement reaction because it follows the single displacement pattern; in your example the H2O breaks up, and some (though not all) of the H is replaced by Na, forming the new compound NaOH. The remaining H atoms join to form H2 gas. Since this shows an atom being replaced by another atom and not forming a new compound, it qualifies as a single displacement. Chemists generally consider diatomic gases such as H2, O2, Cl2, and so on as similar to single atoms in this case.