Now this is seriously complicated.
To begin with, according to the Arrhenius theory, an acid is a substance that releases H+ ions in water, while a base is a substance that releases OH- ions in water. The whole principle of neutralisation was devised by Svante Arrhenius. An Arrhenius Acid is Hydrochloric acid, while an Arrhenius base is Potassium Hydroxide.
The Bronsted-Lowry definition is as follows-
A Bronsted-Lowry acid is a proton donor.
A Bronsted-Lowry base is a proton acceptor.
For example, NH3+H2O—> NH4+ + OH-
So, the NH3 accepts a H+ ion (proton), and is a base, while water here is a Bronsted-Lowry acid.
HCl+H2O—> H3O+ + Cl-
Here, H2O accepts a proton, so its a Bronsted-Lowry base, while water is a Bronsted-Lowry acid.
So, as water acts both as an acid and a base, it is amphoteric. The theory also explains why NH3 (ammonia) is a base.
Lastly, a Lewis acid is an electron pair acceptor, and a Lewis base is an electron pair donor.
For example: BeCl2 + 2Cl- —-> (BeCl4) 2-
So the 2Cl- donates electrons to BeCl2, as it has extra electrons, since it is an anion. Hence, 2Cl- is a Lewis base, while BeCl2 is a Lewis acid.