Explanation:
I.
All kills, no matter what you where in, you killed and which mode you have been in, are always tracked in the "player stats" on the webpage.
II.
There is a peculiarity with kills made in bomber mode: All kills of vehicles show only up on your score card in game. All kills of planes show up only on your score card on the webpage. (That's not the same as the "player stats" page).
Note that in both cases, the kills don't actually count for your score (=rank calculation) at all.
III.
There's a myth that kills in bomber mode show up on either score card depending on the weapon being used (bombs vs guns), but that one is incorrect. (I tested that long ago)