Both Standard electrode potential and
standard cell potential are same thing since the
equation that you gave above regarding Cell potential will still
give the standard electrode potential of any cell in consideration.
Is that so?
Not quite.
Technically, the term Standard Electrode
Potential refers to either the Oxidation
Potential or (more usually, by convention) the
Reduction Potential, for a particular
Electrode (which could be either the
Cathode or the Anode, relative to the SHE), under
Standard conditions.
In contrast, the term Standard Cell
Potential compulsorily takes into consideration both
Redox Potentials, again under
Standard conditions, of both Electrodes (ie.
both the Cathode and the Anode) that
constitute the ElectroChemical (usually Galvanic aka
Voltaic) Cell.
Perhaps the source of many students' (and some school teachers'
as well) confusion, is that the Standard Electrode
Potential = Standard Cell Potential,
if and only
if, one of the Electrodes in
the Cell, happens to be (by deliberate
choice) the Standard Hydrogen Electrode
(SHE).
Because the SHE's Electrode Potential (either/both
Reduction and/or Oxidation Potentials) is designated by humans to
be taken as the default zero Volts (ie. 0
V), hence the Standard Cell Potential for
such a setup (and only such a
setup) = the Electrode Potential for the
Electrode being investigated.
See Wikipedia :
http://en.wikipedia.org/wiki/Electrode_potential