The main difference is that fhìn exists and fhèann doesn't. The nearest I could find in any modern dictionary was feann which means 'skin, flay' as a verb so you could have
chan fheann mi an coineanach 'I will not skin the rabbit'.
But I am guessing you meant fhèin? Mark says
fhìn □ a form of fhèin (see fèin) used in some areas with the 1st pers sing and pl pers prons □ mi fhìn pron myself □ sinn fhìn ourselves
In other words, you can use fhèin for anybody - 'myself', 'yourself', etc. but you can optionally change this to fhìn for 'myself' and 'ourselves' only.
The notes said the same thing except they didn't mention that fhìn can be used for 'ourselves'. Joanne has confirmed that this is an oversight which is being corrected.
I said above 'modern dictionary' because Dwelly (1911) says
In Suth[erlan]d from Strathy Water to Durness, instead of either fhéin or fhìn [...], they say fhèan.
But I am not aware anyone does that now. D
This has been answered at great (possibly too great) length already, but if you want a simple answer:
Myself, ourselves - fhèin or fhìn
Everyone else - fhèin
Note for anyone confused by the pronunciation: this fh is not pronounced the usual way - i.e. silent, but as an /h/. Irish féin (as in Sinn Féin) is also pronounce with an /h/ by some and the Welsh form huna(i)n always has an /h/. So don't think of it as an f lenited for an unknown reason, then pronounced funny, but simply a strange way to spell /h/. D