There are many differences. Here's is just one. You would begin TO READ but commence READING a book.
There are other differences relating to colocations and the level of formality.
I could not imaging someone saying "Lets commence at the beginning", as that seems to ring alarm bells.
Does this begin to make sense? I hope it does not "commence to make sense?"
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Also note that you should not say "Between the both ..." - You can say "Between either of them" or here "There is no difference between them" - (Although is a lot of difference between them and there are lots of differences between them)