Attire is a word that describes a genre of clothing, e.g. Traditional Indonesian attire or evening attire or casual attire. It refers to the whole wardrobe within that genre. It is also very formal.
An Outfit is the collection of clothes worn by one person. For example, today I am wearing boots, jeans, a t-shirt and a cardigan, so that is my 'outfit' for today.
Here is a sentence which I hope clears up the difference:
"I chose a traditional Indonesian outfit from my mothers range of traditional Indonesian attire."
As Sophia said, clothing is most commonly used in English for both meanings.