The two ideas 'self' and 'soul' are not synonyms or different.
"Malunkyaputta, did I ever say to you, 'Come, Malunkyaputta, live the
holy life under me, and I will declare to you that 'The cosmos is
eternal,' or 'The cosmos is not eternal,' or 'The cosmos is finite,'
or 'The cosmos is infinite,' or 'The soul & the body are the same,' or
'The soul is one thing and the body another,' or 'After death a
Tathagata exists,' or 'After death a Tathagata does not exist,' or
'After death a Tathagata both exists & does not exist,' or 'After
death a Tathagata neither exists nor does not exist'?"
"No, lord."
"And did you ever say to me, 'Lord, I will live the holy life under
the Blessed One and [in return] he will declare to me that 'The cosmos
is eternal,' or 'The cosmos is not eternal,' or 'The cosmos is
finite,' or 'The cosmos is infinite,' or 'The soul & the body are the
same,' or 'The soul is one thing and the body another,' or 'After
death a Tathagata exists,' or 'After death a Tathagata does not
exist,' or 'After death a Tathagata both exists & does not exist,' or
'After death a Tathagata neither exists nor does not exist'?"
"No, lord."
"Then that being the case, foolish man, who are you to be claiming
grievances/making demands of anyone?
-- MN 63.3-6 (tr. Thanissaro Bhikkhu)
The Buddha is positionless:
"Vaccha, the position that 'the soul & the body are the same' [OR]
'the soul is one thing and the body another' [ETC] is a thicket of
views, a wilderness of views, a contortion of views, a writhing of
views, a fetter of views. It is accompanied by suffering, distress,
despair, & fever, and it does not lead to disenchantment, dispassion,
cessation; to calm, direct knowledge, full Awakening, Unbinding.
"Does Master Gotama have any position at all?"
"A 'position,' Vaccha, is something that a Tathagata has done away
with. What a Tathagata sees is this:
'Such is form, such its origin,
such its disappearance; such is feeling, such its origin, such its
disappearance; such is perception... such are mental fabrications...
such is consciousness, such its origin, such its disappearance.'
Because of this, I say, a Tathagata — with the ending, fading out,
cessation, renunciation, & relinquishment of all construings, all
excogitations, all I-making & mine-making & obsession with conceit —
is, through lack of clinging/sustenance, released."
-- MN 72.1-15 (tr. Thanissaro Bhikkhu)
I think that this addresses the question sufficiently.