Greek 'Phi'

Why is it that English transcribes 'ph' in Greek origin words as 'ph'
while reserving 'f' for the same sound in Latin origin words? I take
it that it is because Latin did the same, i.e., used 'f' for the sound
in its own words and 'ph' for the same sound in words that came from
Greek. Or, were the sounds same after all? Could it be that they were
different in the old days? Was the sound of Greek 'phi' perhaps an
aspirated ph (p+h) as in the Indo-Aryan languages of India?

Thanks and regards,
Radhakrishna Warrier