I will try to answer your question (I'm a humble student rs)
I research on Internet about your question and I find some information about this.
First, these words are etymologically identical, only one of Germanic root and the other of Latin root.
About the word recognize, It can have two diferent meanings:
The first is when you recognise something because you have seen it before, as in "I recognised the house as soon as I saw it again." In this case, only "recognize" can be used.
The second is in the sense of giving recognition, and in some way accepting its value. For example, one university may recognise that the qualifications of another university are equivalent to their own ; employers recognise certain trades unions but not others ; or I may recognise certain suppliers of a service but not others.
If this second meaning of recognise applies to a person, such as recognising their skill, knowledge or eminence, then the word acknowledge can also be used.
I hope that this can help you.