it's a little bit confusing!
Is it the same concept? or DIF is subclass of MI?
They are the same. However, dif refers to an item, and measurement invariance to a test, collection of items. If you asses dif one item at a time, there's the issue of multiple testing. It is best to approach the problem as a measurement inference problem: are measurements using both tests comparable? If the answer is no... which items show dif? And don't forget effect size... if there is dif/measument non invariance are my results substantively different than if I assume measurement invariance? That, of course, depends on the intended purpose of your analysis
Article Measurement Equivalence and Differential Item Functioning in...
MI sometimes refers to CTT methods, such as MGCFA. DIF is ITT specific, but principally the same.
They are the same. However, dif refers to an item, and measurement invariance to a test, collection of items. If you asses dif one item at a time, there's the issue of multiple testing. It is best to approach the problem as a measurement inference problem: are measurements using both tests comparable? If the answer is no... which items show dif? And don't forget effect size... if there is dif/measument non invariance are my results substantively different than if I assume measurement invariance? That, of course, depends on the intended purpose of your analysis
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