While both Dramatic and Theatrical can mean the same thing, the word theatrical is used in the case of describing something that is exaggerated.
Dramatic is an adjective with multiple meanings.
(i) In one sense it means: staged.
(ii) In another sense it means: spectacular; striking; remarkable; extraordinary
(iii) It can also be used to mean: thrilling; gripping; breathtaking; sensational; exciting
Theatrical is an adjective.
Meanings: exaggerated; over-the-top; artificial; pretentious.
Examples of Dramatic:
(i) 1. The dramatic performance of the artistes was unanimously acclaimed by all who saw it.
2. When the young singer made her dramatic debut in the musical, nobody had expected her to succeed as well as she did.
(ii) 1. The public display of fireworks off the coast was extremely dramatic.
2. In a dramatic manner, the magician pulled cards from the air.
(iii) 1. It was a dramatic reversal of fortunes for the home team as they won all of their last three games after losing the first two.
2. The white water rafting team displayed a dramatic knack of skills & expertise in tackling the ferocious rapids at Dandeli.
Examples of Theatrical:
1. It was obvious that the politician was making a theatrical speech.
2. All the judges were annoyed with the theatrical performance of the models.
3. There was no grace in the ballerina's movements and it seemed more theatrical than natural.