What has less calories wine or a vodka martini?

Calories is basically energy (for you to burn :)

Alcohol has relatively much energy

Half of the sugar ends up in ethanol so image half the weight (100% alcohol) in sugar.

meaning.. if Vodka Martini is mainly vodka then there is more alcohol than in wine and consequently also more calories ... BUT only if it is a dry wine.

If the wine is Sweet then there is suger as well and more calories again... and it could be even.