I've been re-reading all the Kaitou KID arcs (bec I'm obsessed with him like that and I don't have a life) and I realized that though the battle at the clock tower happened before the black star heist, Conan still called and asked Agasa who KID was. This means Conan --when he was still Shinichi --- did not remember facing off with KID (prolly bec he gets what? 10 murder cases in a day?) and yeah they never saw each other's faces during the battle. Shinichi prolly just knew that he was facing a thief that can disguise himself very well.
Still re the clock tower battle, in KID's POV, there was never a mention of him thinking about Shinichi or trying to find out the detective who almost caught him that night (in the MK series and in his thought bubbles in the DC manga. Said thought bubbles are often just side comments of how much he hates Conan for making his escape more difficult).
In the DC Kaitou KID files, it's really Conan obsessed with unmasking KID and not the other way around. (But I stand by what I said that Conan is much more still occupied with BO to start prioritizing the capture of KID -- it's like "Okay if he shows up again, I'll try my best to catch him but I won't go out of my way to look for him")
As for KID, well, in the DC manga, we're rarely given KID's POV but it was mentioned in the Black Star case that KID thought that Conan was just an ordinary kid
However as they meet more often I have to agree that KID is not treating Conan like a normal kid. Maybe he knows that something is up but at the same time we can also assume that he may just think Conan is really talented and smart.
Anyway, summary points -- What we know:
Kaito is not aware of Kudou's existence (never any instances of Kaito trying to find out Shinichi or him trying to find out who he faced that night at the clocktower
Kudou does not remember facing off with KID/forgotten to have faced off with KID at the clocktower battle
KID may not remember Kudou but he remembers the face off (he reminisces said battle right before his first attempt to get the Black Star -- the first time he will face Shinichi as Conan)
Said reminiscence is actually very intriguing bec the fact that he remembered facing off with a certain detective at the clocktower battle and then he meets Conan --maybe he linked them together? (But no, at the end of the Black Star heist, he thought of him as just a "brat")
He is not treating Conan like he is just a normal kid
They like to tease each other a lot with their hinting each other of their personalitiesThey are probably in love with each other
BL: Not enough evidence to prove that Kaito knows who Conan is or maybe said lack of evidence is evidence enough that Kaito is not that
interested in knowing who Conan is.
I agree that he is not the type to go snooping around. If ever he finds out about Conan being Shinichi, I think it will happen very abruptly and not bec he investigated about Conan... and I also think that he will keep Conan's secret especially if Conan explains the whole BO mess. KID is in a similar situation, after all. Also they have helped out each other in several occasions (Magic Lovers case, Eccentric Mansion case) that Conan has let him escape so it is only natural that he keeps it (or use it for his advantage-- such as what he did in the films and even if they are not canon they characters are not OOC)