The distinction I make between invective and abuse is perhaps one that is open to challenge. My dictionary actually defines invective as "abusive speech or writing, vituperation, wordy onslaught or attack". Though dictionaries shouldn't be treated as being the last word...

But I'm sure you'd recognise as familiar the example given below the definition: he was a master of invective, but a shallow reasoner There's a lot of that around here sometimes.