"mientras/mientras tanto" and "entre/entre tanto" are really different. I'm sorry to say the contrary regarding to the other people who commented above, but those words aren't the same, and only could be used with similar meanings in 2 cases. Those cases are where the words (in english) is "meanwhile" (mientras tanto/entre tanto) and "while" are used. I mean this:
Meanwhile-----> mientras tanto / entre tanto (but "mientras tanto si the best translation)
While-----> mientras/ entre (but "entre" is often used like a slan way of talking at certain countries)
I'd advice you that you should study "mientras" and "mientras tanto" firstly, and and when you understand the usage or those words, "entre/entre tanto" will be more easier than how these are currently.
I don't know how to explain exactly the meaning of "mientras tanto" and "mientras", but I could say you that the translations are "meanwhile" and "while" respectively.
I hope I have reponsed your question :)