Question

"in an electrochemical cell, electrons are generated at the"

Answer 1

In electrochemical cells redox reactions are involved

  Zn(s)  +  CuSO4 (aq) → ZnSO4 (s)   +  Cu(aq)

The above equation can be split into the following two half cell reactions
   Zn (s) →  Zn+2 (aq)  +  2e-  (anode)
  Cu2+ (aq) + 2 e-  → Cu(s)  (cathode)

When the anode and the cathode half cells are connected by a wire, the electrons which are generated at the anode flow to the cathode. This flow of electrons constitutes an electric current and hence the electrons are the charge carriers.

In electrolytic cell, the electrical energy is used to drive a chemical reaction. As an example consider the electrolysis of molten NaCl. The Na+migrate towards the negative electrode and the Cl- migrate towards the positive electrode.
  Cathode: Na+ + e-  → Na
   Anode: 2 Cl- →  Cl2 + 2e-

The electric current is due to the migration of the ions towards the oppositely charged electrode. Hence in galvanic cells, the electric current is due to flow of electrons and in electrolytic cells due to the migration of ions. Therefore these are the charge carriers. Since protons are not formed in the cell, they are not involved in the reaction and are not the charge carriers.