Yes in this case they really are the same. Students are often confused betweeen these tenses as natives swap between using them with very little difference in meaning. The main difference is I have studied English for 6 months = The focus is on the result (therefore your English has improved over the 6 months).
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AnonymousThe 1st sentences imply you are still study and living, where as the 2nd sentences may imply that you have just finished.Not always.
cathyregarI think its "for".Yes it is. With the present prefect we express time with for and since.