Learn English – The use of “travel” as a noun in some restricted cases

Technically they are the same but there is perhaps a slight implication with the latter that the something in questions is not being used, being underused, or would henceforth not be used and that one is taking advantage of an opportunity. For example:

I used the eggs.

pretty straight forward.

I made use of the eggs.

implies, perhaps that they would have gone bad had I not used them or that no use had been thought of previously.

The difference lies partly in the physical properties of the different nouns, and partly in their intended use.

A mesh is what all these terms have in common; it's a weaving of some thread-like substance into a regular-polygonal pattern (typically the polygons are squares, but not necessarily). The polygons are generally expected to all have equal size, and any type of weaving involving non-polygonal patterns - a knitted sweater for example - is not considered a mesh. A window screen for keeping insects away is a good example of a mesh; a metal chain-link fence is a good example of one not based on squares.

A grid is a mesh that's flat - for example, U.S. city streets are usually organized in a square mesh pattern, but we call this pattern a grid because it's basically flat (the earth it lies on is flat).

A net is a mesh that is not necessarily flat; it's made of flexible material. Thus, fishing nets can be wrapped into a bag-like shape for hauling in fish. This also explains, as you asked, why we say mosquito net and not mosquito mesh - although mesh could be sort of appropriate if we're talking about a fixed mesh (like the wall of a tent), intended to keep mosquitos out but not intended to be used for catching them (as a net would be used).

(So in general: we say net if we're talking about a mesh whose purpose is to capture, contain, or exclude something.)

Finally, a network has the least in common with the above three because it doesn't necessarily follow a regular pattern. Network never refers to any of the above terms; it refers to irregularly patterned systems of connection. Computer networks, for example, contain many connected computers, but their physical proximity to one another is completely arbitrary.