I am wondering is gascolator the same as fuel strainer, or this two things are bit different. Because sometimes I see one term, sometimes another, and I don't know if I am reading about the same thing.
Yes in practice they are the same thing (it's surprisingly difficult to find the origin of the term "gascolator") and most definitions will mention both terms, although I tend to think of the gascolator part as the gravity water separator bowl/quick drain component, and the strainer as the filter screen covering the outlet.
Back when cars had them (up to the early 60s) they were called "filter bowls" with the bowl part made of glass and without the quick drain. You just removed the bowl to get rid of any water you saw when checking under the hood (airplane gascolators from the 40s also used glass bowls, although most have been replaced by metal ones).
Most aircraft gascolators use a 75 micron mesh screen (the strainer part - about like the screen on those plunger coffee makers) at the top of the housing to keep particles from passing to the carb. On my homebuilt I improved on that by using a 30 micron sintered bronze filter made for the filter bowl of a late 50s Chev Impala, which fits perfectly in the standard gascolator bowl.
Short answer: In practice they are often considered the same device, however they are really different devices.
The gascolator is used to separate different densities. Water is the normal objective, however tank sediment (sand, particles of sealant and other debris) are secondary objectives. The gascolator, of necessity, should be at the lowest point in the fuel system.
A fuel strainer is normally a screen or other mechanical filter, which separates by virtue of particle size.
Often the design of these devices are done so that a strainer screen is flushed by fuel sampled from the gascolator, preventing obstructive build up of debris.
In many small single engine and light twin engines, the thing often called the gascolator is just that, and has minimal straining function. A risk is straining is that the strainer could get clogged with contaminated fuel. Such a clog can prevent fuel flow, and cause fuel starvation of the engine. Generally it is desirable for an aviation engine to accept fuel with some particulates rather than experience fuel starvation due to a clogged strainer.
So in the end, what has traditionally been called a gascolator is implemented, and an absolute particle size strainer is not as common or strains for a relatively large size.