"of course, both are same" Is this phrase correct as written? (while explaining about two things)
Again, without knowing the context of this sentence, it is extremely difficult to provide more than mere grammatical advice. However, if yours is a comparison/contrast assignment, it may be better to use the word similar rather than the same since rarely are two things, circumstances, people, ideas, etc. exactly the same. Usually, they only share some points that are the same--not all. Therefore, the word similiar is more appropriate.
If you search for transition words, you should be able to find these important connecting words for comparison/contrast essays and such that will enable you to set up the differences and similarities that you want. There is one site listed below which can be of help to you.
Also, see the enotes topics section since there are aids in writing such things as comparison/contrast essays. One of these is also listed for your convenience.
The only thing that is clearly wrong about this sentence is that it needs a "the" between "are" and "same." In other words, it needs to say "of course, both are the same." You cannot say "they are same." Instead, you must say "they are the same."
Without knowing what the rest of your paragraph is saying, I cannot tell you for sure that this sentence is now perfectly correct. It may not go properly with the sentences that come before it. However, just on its own, it is a grammatically correct sentence once you put "the" in.