Their is not an adjective. Their is a determiner:
It's their house.
It's their car.
It's their business.
We use theirs when the object is left out (instead of the noun you put the ending -s):
Our house is number 25, and theirs is just opposite. (taken from Longman Dictionary)
There are at least two ways these terms can be used:
1) They can be used to indicate assent:
For example:
We need some more eggs to make the soufflé. Can you go buy some?
Alright. (or, Okay.)
2) They can be used to indicate that the quality of something is "satisfactory but not exceptionally or especially good":
For example:
How was the movie last night?
It was okay. (or, It was alright)
In these two contexts, I find these terms pretty much interchangeable. In the first, you agree, but without any particular eagerness. In the second, they both convey about the same sense of enthusiasm (or apathy).
I will offer an opinion that differs slightly from Mowzer's: I think they are both somewhat general and informal terms. If for some reason more formality, politeness, or precision is called for, I would recommend using different words altogether. For example:
Judge: I'll need you to approach the bench and take the oath.
My response: Yes, your honor. (not, "Alright" or, "Okay")
English Professor: What did you think of the Faulkner story you read this weekend?
My response: It has a good message, but it's a little dry. (not, "It's alright" or, "It's okay")
Girlfriend's mother: We need some more eggs to make the soufflé. Can you go buy some?
My Response: I'd be glad to. (not, "Alright" or, "Okay")
I think your question is a fair one, and your analogy is a good one. But, in this case, I think the two words are much more interchangeable than, say, broke and bankrupt.
Best Answer
In grammatical terms, their is a possessive determiner, just like my, your, his, her, its and our. It indicates that what is described in the following noun phrase belongs to, or is in some other way associated with, the person or thing to which the possessive determiner refers. Just as my car is a car that belongs to me, so their house is a house that belongs to them.
There is a word with many uses. In your example, There are lots of skyscrapers in Dubai, it is what is sometimes called a ‘dummy subject’. It would be grammatical to say Lots of skyscrapers are in Dubai, but, generally, we don’t. We use there are (or there is) where French uses il est or il y a, German uses es ist, es sind or es gibt and Spanish uses hay.