As I know so far, mortar and grout are mixtures of cement paste and fine aggregates, but both of them play different roles in the construction site. Is it true that grout has more strength compared to mortar? What are the differences between them?
Mortar is used when you want materials to adhere to one another, as in brick laying or tile placement. Grout however is a material that is meant to flow, sometimes under pressure. The main purpose of using grout is to serve in situations where you need to fill gaps or holes that exist due to construction techniques (such as concrete cooling in huge masses of concrete or structural support on climbing formwork). The purpose of using both materials are different, although they are in essence made of the same components. As for resistance I would say it depends on the situation, I wouldn't say that grout has more strength compared to mortar without having a bit of context.
Also, you might define a bit better what you mean by "strength", one material can be more resistant to compression while the other more resistant to traction, so there isn't a direct comparison between the materials without having a bit of context on what applications you are using it for.
In general grout is used for filling gaps between courses of bricks, blocks or tiles usually once they are in place for a combination of environmental resistance and cosmetic appearance. The main purpose or mortar is the structural bonding of laid blocks as they are laid, usually a combination of adhesion, load distribution and levelling.
In practice this covers a huge range of materials, of which cement based ones are a fraction. For example there are a whole category of materials based on lime which can be used as mortars, grouts, renders and restoration/repair putty or indeed as castable media.
In reference to the comment from Ethan48 you could extend this definition by saying that mortar tends to be a stiffer and more plastic formulation used as a sort of 'glue' whereas grout is finer and (relatively) more fluid for use in filling gaps in assembled structures.
Assuming cementitious binder, then:
Grout = cement:water
Mortar = cement:sand:water(:lime)
Concrete = cement:aggregate:sand:water
My dictionary states that people mistakenly refer to grout as having sand.
Mortars are usually weaker than the product it binds so that they get damaged first because mortar is usually cheaper to repair. Grout is usually as strong as the material it binds.