I checked synonyms of floor - ground, storey, tier, deck, mezzanine. Upon checking the meaning of each one I detected that only tier I am not able to use in sentence where the meaning is floor. I know tier as grade. Please advise if you can give me an example of tier as floor.
Several of those words has multiple meanings, and they don't all intersect with 'floor' on the same meaning.
'Floor' has two main noun meanings, closely related. It means the surface that people stand on, or a distinct vertical level of a building. It has related verb meanings as well - it can mean: to cover a floor or sub-floor structure with a flooring surface, to form a floor; to knock something or someone to the floor; to stop someone in their tracks (by metaphor for the previous meaning); to silence someone, such as by providing a compelling argument (by metaphor for the previous meaning); to amaze or surprise (by metaphor for previous meanings); to finish or make an end of (by metaphor for previous meanings); or, in mathematics, to set a lower bound. There's also some other specialised noun meanings as well, but we don't need to go into those.
'Ground' is mostly only the surface that people stand on, and usually implies that it is either a natural surface, a natural surface with some covering outdoors, or at the same level as the surface outdoors. There's at least one related verb meaning.
'Storey' mostly only means a distinct vertical level of a building.
'Tier' means any sort of (usually vertical) level of any structure, including abstract or conceptual structures. Its use overlapping with 'grade' is for an abstract or conceptual structure. So if you have a physical structure with levels, those levels can be referred to as tiers.
'Deck' has a complex set of meanings that largely correspond to 'floor' but in specialised situations, such as on ships or aircraft, and then idioms that derive from those (such as "hit the deck").
'Mezzanine' generally refers to a storey that is between other stories - you have the first floor and the second floor, say, and a mezzanine between them (usually off to one side, with the access to it half-way up the stairs between the other two floors).