Is an acid a salt or not?
It is a semantics question with an open ended discussion. If you recall the old problem "How many angels can dance on a pinhead? Medieval problem, this issue here is similar.

Basically in chemistry, all the terminology is controlled or endorsed by the International Union of Pure and Applied Chemistry (IUPAC). They have a very open ended definition of a salt: "A chemical compound consisting of an assembly of cations and anions."

If we follow some really old chemistry texts (>1850s), yes an acid was defined as a salt of hydrogen ion, i.e., an acid is a salt whose electropositive element is hydrogen Definition of an acid.

Did this definition by a few chemists become popular? The simple answer is no. Not in a general sense. 

The modern interpretation of an acid, again from IUPAC is, "A molecular entity or chemical species capable of donating a hydron (proton) or capable of forming a covalent bond with an electron pair."
If you have heard of ionic liquids, they consist of a large organic cation and an anion, this is a salt as well.

Then you have so-called acid salts, such as sodium hydrogen sulfate e.g.,  $\ce{NaHSO4}$. Their pH is very acidic and these "salts" will neutralize bases like a typical acid.

Thus one may loosely say, that all acids may be considered as salts but not all salts are acids.