What is the difference between monolithic and non-monolithic dc-dc converters? For example this is monolithic dc step down controller: LTC3609
Monolithic in the sense of the part you have refers to the fact that the power switch(es) is(are) integrated into the controller IC as a single part. There are cases when you have to purchase the switches as external components.
In my opinion, a truly monolithic converter would be one that also integrates the inductor and possibly even the capacitors. I mean, look at all the stuff you have to add for the converter to work!
To be a little more specific, monolithic in this sense usually means that the power switches (FETs usually) are on the same silicon die as the control circuitry.
There are also converters that have several die in the same package, e.g. a controller and 2 FETs for a sync buck. This might be transparent to the user as from the outside it seems like a single IC, but it is not referred to as a monolithic part.