Are Islamic and Jewish dietary laws the same?

Yes, they do. They have foods which are 'Halal' which are foods that they are allowed to eat and 'Haram' which are foods they aren't allowed to eat.

They are not allowed to eat pork, because they thought that pigs were dirty animals and were not fit to be eaten. They're not allowed to eat meat from animals that have died from natural causes. All the animals which are slaughtered have to be cut quickly across the throat because this is the most painless way for them to die and it drains most of their blood (Muslims are not allowed to eat blood).

They are also not allowed to take drugs and drink alcohol.