Mostly we say : سرم شلوغه Both are correct

It needs a verb, so we should say «سرم شلوغه», not «سرم شلوغ». They both mean "I'm busy", but a) «سرم شلوغه» is informal. b) You can mention the activity that made you busy with «مشغولم»; for example: مدیر مشغولِ (یا مشغول به) حل مشکلات بود The manager was busy solving the problems.

Probably You mean: are these two words the same by "همینه" which is not correct question in Persian, You should say یکیه rather than همینه in such cases. So instead, say : »مشغولم" و" سرم شلوغه" یکیه؟" = Are "مشغولم" and "سرم شلوغه" the same? The Answer is Yes, they are the same.= بله یکیه/ بله یکی هست

سرم شلوغه is mostly used in situations that you are busy and مشغولم or مشغول ...هستم could be used in both formal and informal expressions...for example: آتش نشان ها مشغول خاموش کردن آتش هستند / من مشغول تصحیح کردن برگه های امتحانی هستم/ بچه ها فعلا مشغول امتحاناشون هستن و نمی تونن بیان/ فعلا مشغول برنامه نویسی واسه یه شرکتم سرم شلوغه is more common for expressing being busy more than مشغولم in conversations but مشغول ..هستم is used for both formal and informal and depends on the sentences and situations: A: می تونی الان بیای پیشم؟ B: نه متاسفانه، خیلی سرم شلوغه الان...ای کاش قرار رو بزاریم واسه فردا (in this case سرم شلوغه is more common than مشغولم) A: دلم خیلی واسه دخترت تنگ شده، چیکار می کنه ؟ B: دخترم فعلا مشغول امتحاناش هست و ایشالله امسال هم مثل همیشه شاگرد اول بشه ( in this question she won't answer: دخترم سرش شلوغه because she is explaining about the reason of being busy : مشغول امتحانات بودن (busy by exams)) So, in general you can translate with this method in informal conversation: - I am busy : سرم شلوغه (it is used more common than مشغولم) - I am busy with..: مشغول ...هستم There is another phrase : ذهنم مشغوله that means: ''my mind is engaged'' and completely is different from: سرم شلوغه