this is one of those cases where if you google the word you'll see the other word inside the definition. It can make finding a definition for it a bit harder- BUT if you ever try googling things in English and see it happen it means for the most part you can use the words the same way
"the water covered the stones completely"
"the water covered the stones totally"
"I was totally down with the plan"
"I was completely down with the plan"
they both give the idea that you are 100% in agreement, or something is 100% done. No one would notice the difference if you had to pick one or the other.
If you did want to know the difference: As adverbs the difference between totally and completely is that totally is entirely; completely while completely is (manner) in a complete manner; fully; totally; utterly.
they even use the words on each other when trying to explain the difference so that just shows how similar they are