The second version "I'm going to the beach" could imply they are leaving right now. Whereas the first version would imply you're going to go to the beach in the near future, such as this afternoon.

going to go = I will go there in the future. am going to the beach - could be used either for the present (I am going there now), or in the future, usually in response to a question about some future time. "What are you doing Saturday?" "I'm going to the beach." OR "I'm going to the beach on Saturday." OR "I'm going to go to the beach." All are a correct answer to the question. Confusing, I'll admit. English tenses are a pain, partially because the rules seem so vague.

I meant to say that Be + going to + infinitive is used for future plans, arrangements and predictions example : It's going to rain tomorrow - prediction I'm going to work during the summer - plan I'm going to meet my friend after work this evening - arrangement We often use a future time expressiion with this tense.

They both mean the same - for example: Be+going to+infinitive I'm going to go to the cinema, or I'm going to the cinema These 2 sentences mean exactly the same - When the verb GO is the infinitive you can use it or omit it, both are grammatically correct. I'm going to swim in the sea - in this sentence you must use the infinitive in order for the sentence to make sense. I hope this helps!