So this one doesn't look normal to me. What does look normal is a euro cylinder. You can leave a key on the inside with it locked, if the key is inserted but not turned you can still use a key from the other side. If the key is turned slightly, a key from the other side won't work.

If you are really concerned about getting locked in, you can get euro cylinders with a thumb turn on one side and key on the other.

What makes them great is to change the cylinder you open the door, remove one screw, put in the key and rotate about 20 degrees and the whole thing slides out, takes about 5mins to change a lock. Cheapest low security go for about £10 all the way to high security special profiles for ~£80