Looking at it again, it’s not a good diagram, I just found it on the web. In the gwr system, the condenser is in the cab roof, so there is a constant head of water between that and the oil container pushing the oil out into the propellant steam supply. Hence the name hydrostatic.
The difference from displacement is that hydrostatic is fed with boiler pressure saturated steam and has the propelling steam, whereas displacement would be fed by superheated steam at steam pipe pressure and no propellant. Actually I’ve just realised that Richard’s drawing is different to most displacement lubricators I’ve seen in that usually there is only one connection to steam pipe, the steam goes in the same hole as the oil comes out, so it’s a sort of cross.
Thanks Duncan, I guess the basics is that in a hydrostatic lubricator the driving pressure is from a constant head of condensate in a tank, hence hydrostatic, whereas a displacement lubricator is driven by live steam creating the condensate in the lubricator. It may not necessarily be superheated, particularly in many model steam plant. The difference then being that the driving pressure isn’t static, it varies with the steam output from the boiler.
Even in the niche area of model boats there are many different takes on what may be considered a displacement lubricator. From the most basic straight through connection with no drain facility:

To a straight through type again with no drain facility but incorporated into the engine:

To the type described where the steam going in is a common connection to the oil coming out, now with a drain connection:

To a straight through type with its own built in drain valve and needle valve control of the oil:

To the most sophisticated with needle valve control, built in drain valve and a glass body so the oil can be seen:
