Honour is a status other people grant you — it can be given, withheld, or taken away. Philotimo is a debt you set for yourself and then quietly pay, whether or not anyone notices. Which is why one is about reputation and the other is about what you do when there's no audience.
Side by side
Aspect
Philotimo
Honour
Granted by
Yourself
Others
Needs witnesses
No
Yes
Can be lost
Only by you
By anyone
Originally meant
Ambition
Standing
What each one means
Philotimo
Philotimo is the internal obligation to do the generous and right thing because of who you are, with no expectation of return — a word that carried both senses in antiquity — vainglorious ambition in one register, honourable ambition and lavish public generosity in another.