They're not the same thing. One can usually not use the word frei (which mostly means “free” in the sense of independent, unbound, without handicap or unoccupied) to say that something doesn't cost any money.
Rather, one would either use the word kostenlos (literally “costless”) or umsonst. Note that the word umsonst also has the meaning of “for nothing” (in the sense of a wasted effort) and thus it’s safer to use for free products rather than services.
Examples
Die Bücher sind kostenlos. – The books are free.
Das sind kostenlose Bücher. – Those are free books.
Die ganze Mühe war umsonst. – The whole effort was for nothing.
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Other Common Ways to Say Free
Another word used to indicate that something does not cost money is gratis. You may see this word when shopping to indicate a free gift, or that something is complementary.
It's also common to see boxes or items on the street with a sign that says zu verschenken, which translates to “to give away”, and means that the items are available for anyone to take for free.