No, they are not the same. An equitable charge is stated as such to distinguish it from a legal charge. And by definition, a fixed charge is a legal charge.
“Equitable” suggests that it’s not a formal, legally enforceable charge – it’s rather more INformal and exists in equity ( ie, in fairness )
I don’t know if that’s come out as clearly as I had hoped. Is it any clearer for you?