A defining feature for acids / bases
tl;dr version: You can only define an acid or a base in context of a reaction. Individual compounds are not acids by themselves. They are acids in reactions in which they lose protons (or gain electron pairs).

The Lewis definition is the broadest acid-base definition. Each of the others are specific subsets.
The Arrhenius definition is the simplest:

Acid = something that creates $\ce{H+}$ ions in water.
Base = something that creates $\ce{OH-}$ ions in water.

Thus any compound that can ionize in or react with water, like $\ce{HCl}$ or $\ce{HCO2H}$ is an acid and any compound that contains hydroxide ions or reacts with water to produce them, like $\ce{NaNH2}$, is a base.
However, the Arrhenius definition breaks down in non-aqueous media.
The Brønsted-Lowry definition is broader and more inclusive.

Acid = proton donor - All Arrhenius acids are Brønsted-Lowry acids
Base = proton acceptor - All Arrhenius bases are Brønsted-Lowry bases

The Brønsted-Lowry definition allows us to extend our discussion of acids and bases to, say, solutions in methanol $\ce{CH3OH}$. Note that the Brønsted-Lowry definition requires a proton transfer reaction to be occurring to properly identify acids. For example, water is amphiprotic - it can react as either an acid or a base. Many other compounds are similar. There is no absolute &quot;this is an acid always&quot;. Instead, you have &quot;this compound is an acid in this reaction&quot;. For example, water is an acid in the first reaction and a base in the second.
$$\ce{H2O + H- -&gt; H2  + OH-}$$
$$\ce{H2O + H2SO4 -&gt; H3O+ + HSO4-}$$
The Lewis definition is broader and more inclusive still. It allows extension of acids and bases into aprotic media and situations:

Acid = electron pair acceptor - all Brønsted-Lowry acids are Lewis acids
Base = electron pair donor - all Brønsted-Lowry bases are Lewis bases

Again, the Lewis definition requires a reaction to occur in order to classify compounds.
However, in all cases, there are compounds that behave as acids much more frequently than they act as bases, and vice versa. For example, $\ce{HNO3}$ is almost always an acid, but not exclusively. The first step of the mechanism of aromatic nitration is considered to be a proton transfer step between sufluric acid and nitric acid in which nitric acid is the base.
$$\ce{HOSO3H + HONO2 &lt;=&gt; HOSO3- + O2NOH2+}$$