Yes, you're quite right about the spelling (though 'whiskey' applies to everything except Scotch, i.e. Irish, Canadian, Bourbon, etc.), and that the difference between Irish Whiskey and Scotch Whisky is in the malting. In case you're interested, the exact difference is as follows:
In order to halt the malting of the barley, it is dried in kilns. For Scotch, this takes place over a fuel that includes peat, whose smoke imparts the 'peaty, smoky' flavor characteristic of Scotch. For Irish Whiskey, the malted barley is dried in closed ovens, and never comes in contact with smoke, which results in a more 'pure' malted barley flavor, without the 'smokiness' of Scotch.