Differences between phenols and alcohols
Nope. Alcohols consist of an -$\ce{OH}$ group bonded to a saturated carbon ($\mathrm{sp^3}$ hybridized, no multiple bonds).
IUPAC says:

alcohols
Compounds in which a hydroxy group, -$\ce{OH}$, is attached to a saturated carbon atom $\ce{R3COH}$. The term 'hydroxyl' refers to the radical species, $\ce{HO^.}$.

and

phenols
Compounds having one or more hydroxy groups attached to a benzene or other arene ring, e.g., 2-naphthol:

(source: iupac.org)

A phenol consists of an -$\ce{OH}$ bonded to an unsaturated $\mathrm{sp^2}$ carbon. Thus, it does not qualify as an alcohol. One can classify it as an enol, though.

Really, to me, the classification doesn't matter. Classifications are artificial, what is important is, how well the properties fit in the classification.
Many of the alcohol properties depend upon:

Its unsaturated nature: oxidation to ketone/aldehyde/acid
The weaker $\ce{R-O}$ bond and its ability to easily break and form an $\ce{R+}$ cation (this makes it a good participant in $\mathrm{S_N1}$ reactions)

Phenol can obviously not be oxidised at the $\ce{OH}$ to a ketone/acid (though one can do stuff to make it into a quinone). Phenylic carbocations are unstable, thus we don't get any $\mathrm{S_N1}$ reactions, and the $\ce{Ph-O}$ bond stays put.
On the other hand, most of the reactions of phenol depend upon its

Aromatic phenyl ring: All the EAS reactions
Weaker $\ce{O-H}$ bond (i.e., acidic nature): Reimer-Tiemann reaction, etc.

Thus phenols and alcohols don't have too many reactions in common. So, in this case, they have been classified in a sensible manner--if phenols were classified as alcohols, we would basically be clubbing two radically different classes of compounds under one umbrella.