I suppose that the salient difference between the oxygen and sulfur atom in organic chemistry is the nature of the carbon oxygen vs. carbon sulfur bond (both single and double). Both of them are covalents, but the first is a polar covalent bond (see the difference in electronegativities). The latter is more interesting: although there is no big electronegativity difference, the weaker orbital overlap causes that e.g. 1, the thioamide carbon atom is more electrophilic than the amide and 2, ester carbon atom is less electrophilic than the thioester carbon atom. As others mentioned earlier the electron structure is diffuse around the sulfur which makes a thioalkoxide a ‘soft’ base whilst an alkoxide is a hard base. So it can be attacked easier by soft alkylating agents such as alkyl-iodides.