Brazilian Portuguese: Here is a picture showing you the difference: http://chanticleersociety.org/cfs-filesystemfile.ashx/__key/CommunityServer.Discussions.Components.Files/17/7802.Limao-lima-e-Siciliano-copy.jpg
Here is how a user in that forum explained it:
A Lime is called Limão;
A Lemon is called Limão Siciliano;
A Key Lime is called Lima da Pérsia or just Lima (I guess you call this key lime).
The picture really shows it better. For fun: caipirinhas are made with limão (lime), and your cola soft drinks come with a slice of limão. And limonadas (lemonades) are made with limão as well. Hope it helps!
The picture they used for the Lima de pérsia or lima looks like an orange to me (key limes just look like tiny limes). But looking up the scientific name yields a key lime, so I think they just used the wrong picture. They're called key limes because they grow well in the Florida Keys. Thanks for the reference
In central and south American Spanish speaking countries, limes are called 'green lemon' or 'limón verde' (This is confusing since they are not the same fruit and lemons are green before they are ripe!). The same is probably true in Portuguese, so a lime would be 'limào verde'. I also guess that when it's clear which one you mean, this may be shortened to just 'limão' .
I've also heard that in many areas of South America you won't find lemons, but limes are common and that here they are simply and incorrectly called 'límon/limão/lemon'.