What is the difference between the 10 commandments and the other 613 laws, and which of the 613 laws in the Torah are still applicable?

The 10 Commandments are really ten categories of commandments into which all the 613 commandments can be subdivided. They are all still applicable except for those commandments whose performance has been taken out of our control, such as those relating to sacrifices, the Temple service, some of the agricultural laws, etc. Also because we no longer have a Sanhedrin (a Jewish High Court), corporal punishment, such as lashes and the death penalty, is no longer administered.