The answer is simpler than you'd think.
There are just two categories of countries which take the definite article:
1. Names which are plural nouns : the Netherlands, the Philippines
2. Names which are common nouns ( like 'state') preceded by an adjective : the United Kingdom, the Czech Republic, the Russian Federation
and (obviously) names which fall in to both of the above categories: the United Arab Emirates, the United States
This is a simple grammatical rule - nothing to do with abbreviations.
If you put 'the' before a place name, this suggests it is a region, for example, 'the Yukon' or 'the Camargue' . As Nicholas has pointed out, it is offensive ( and inaccurate) to refer to Ukraine as 'the Ukraine', suggesting that it is not a sovereign state. If you refer to the location of Kiev as being in Ukraine - not 'the Ukraine' -you are being both grammatically and politically correct.
The only country which doesn't fit this is the Gambia, a little country of only 2m inhabitants in W.Africa. I don't know why the Gambia is the Gambia - perhaps because it's also the name of the river. Unless you have occasion to go to or talk about this one country ( I know that I never have), I wouldn't worry too much about this one exception to the rule.
And yes... if you're talking about the major city called Toronto, it's in Canada - a great big country in North America which is NOT the United States. There are a handful of tiny little places in the US which also happen to to be called Toronto, but I doubt if you'd have heard of any of them. Most people haven't.