You are dozing if you are sleeping lightly, and can be easily woken up.
When you are asleep, sometimes you dream. Dreams are a little like a movie that plays in your head while you sleep. Sometimes dreams are very ordinary, sometimes they are exciting, and sometimes they are scary. Scary dreams are called nightmares. Often things happen in dreams that aren't possible in real life.
A nightgown, nightdress or nightie, is something you wear to sleep in. Only girls and women wear nighties.
A nightmare is a bad dream. Nightmares can be extremely frightening, and make you wake up scared.
You might also use nightmare to describe a particularly bad event, for example "we had a nightmare vacation".
Pajamas, also spelt pyjamas or just PJ's are clothes that you wear at night when you sleep. Pajamas can be worn by girls, boys, men or women, but nightgowns are only worn by girls and women. The lady in the picture is outside in her pajamas.