Oxidation of alkylbenzenes is different than oxidation of an alcohol or double bond, or at least in part. The oxidation of an alkylbenzene is a radical reaction and is often (generally) done with heat. The product of that reaction is an alcohol or something that is oxidizable.
Oxidation of an alkenylbenzene or alkynylbenzene is like an electrocyclic reaction. You can draw a cyclic intermediate for the reaction of ozone, MnO4(-), or OsO4. If the manganate cyclic ester is not hydrolyzed, it can decompose with cleavage of the C-C bond. If styrene were being oxidized, the intermediate would be benzaldehyde. If water is present, it will form a hydrate which is a geminal dialcohol. Oxidation of it gives a carboxylic acid.
If you were doing an oxidation under mild conditions, ketones are not oxidized further as a methyl group will not give up electrons as easily as loss of a proton.
PhCH(OH)O-X ---> PhC(OH)=O + X- + H+
PhCCH3(OH)O-X -X-> PhC(OH)=O + X- + CH3+
This requires more vigorous oxidation conditions to form an enol or peroxide (Baeyer-Villiger type) for further oxidation.
This is a little sketchy and brief, but if you understood the how alkylbenzenes oxidize and know how the other groups can oxidize, this should explain the difference.