If I say "Be careful when you talk to Alice about her husband, because she just got divorced and she'll be hurt or uncomfortable", then I have conveyed that complete thought to you. Nothing is implied because I have stated clearly that you should not talk about Alice's husband to her and I have also stated clearly the reason that you should not do it. However, if I say, "Be careful - Alice just got a divorce," I have not said directly that you should not talk about her husband to her, but I have strongly implied it. I have communicated the idea, but have not said everything directly. So if I imply something, I am conveying it. However, if I convey something, I could be either saying it directly or implying it.

Salam. I wish to convey (give) my deepest sympathise to you. ----------- Me - Don't worry, I'll wash the dishes tonight, I'll be doing them anyway. You - What are you implying? (suggesting/trying to really say) Me - I'm implying that you never do the dishes. Convey is me saying something directly, imply is me saying something without actually saying it. "Darling, would you like to wear the blue jeans with that top?" Is implying that I don't like the black jeans with that top. Craig, I wish you would just convey to me what it is that you mean to say! Ok Arwa, I don't like the black jeans. Convey and imply shouldn't really be thought of in the same way, I'd never swap a conveyed message with an implied one.