"That office on the third floor is like this one."
Translation:Az az iroda a harmadik emeleten olyan, amilyen ez.
OK, let's think about this. There is a certain difference, but it is only apparent in some cases. That is, "mint" and "amilyen" are interchangeable in most cases.
Here is the literal difference, and forgive my English:
"Ez az autó olyan, mint az az autó."
"This car is like that car."
"Ez az autó olyan, (mint) amilyen az az autó."
"This car is like (what) that car is like."
That is, with "mint", we are comparing one thing to another thing. But that thing can be pretty much anything, not just actual things.
"Ennek az autónak a színe olyan, mint annak az autónak a színe."
"The color of this car is like the color of that car."
With "amilyen", however, we are comparing what one thing is like to what something else is like.
Again, most of the time these two mean the same thing.
But sometimes we specifically compare things to what something else is, or was, like. For example, if that likeness is temporary, changing, etc.:
"You are like you were like when I first met you."
"Olyan vagy, amilyen akkor voltál, amikor először találkoztunk."
Well, maybe we can use "mint" even in cases like this one.
And, actually, we can think of both of them being there:
"mint amilyen" - with one of them potentially omitted.
There is a saying, a proverb:
"Amilyen az adjonisten, olyan a fogadjisten."
"What the 'Hello' is like, that is what the 'Welcome' will be like."
That is, the way you treat others will be the way they will respond to you, or behave with you.
But this leads us to my second point:
When the "olyan" - "mint/amilyen" clauses are swapped, then we are much more likely to use "amilyen", and not "mint".
"Amilyen az az autó, olyan ez az autó."
"Mint az az autó, olyan ez az autó."
Mind you, this is not necessarily wrong, but it is highly unusual.
Now, this "olyan - amilyen" pair is just one of the countless other comparative pairs:
"úgy - ahogy"
"akkor - amikor"
"azért - amiért"
"onnan - ahová"
"azért - amit"
Etc., etc., the list is endless.
The word "mint" is usually only used to replace "amilyen", not any of these other ones.
And you can think, if it helps, that there is potentially a "mint" in front of the second element of each of these pairs, only it is omitted:
"úgy" - "(mint) ahogy"
"akkor" - "(mint) amikor"
But this is just in theory, please don't start talking like that. We don't need a "mint" in there. You can use it for "amilyen", and a couple of others ("úgy" - "mint/ahogy" has good potential), but that's about it.
Because its place can vary. It is a reference point to the second clause. It works similarly to "such".
"That office is such ... as ... "
"Such is that office ... as ..."
Something like that. So, it can move around according to the same rules as a regular adjective or adverb would move around. Except it is referencing another clause.