[AdiDex]

In galvanic cells
cathode is positively charged let me take an example of galvanic cell.

Cu²⁺ + Zn(s)  Cu (s) + Zn²⁺

in cathodic compartment Cu²⁺ is getting reduced and getting stick to the cathode. so we are giving it positive sign and its potential also get high as accumulation of positive charge is happening.  Just opposite of it will happen in case Anodic compartment .
so we concluded Cathode High Potential  positevly charged
                       Anode     Low potential    Negatively charged

so now let me give an example of electrolysis .
a electrode is connected to negative  terminal (Anode) of battery is called cathode as it is cathode here ions will get reduce...
we connected it from anode but it will act as cathode .

is this only because of  we are only considering the system containing the process of electrolysis ?? We do not care that from which terminal of battery it is connected , just reduction is happening so it is cathode and if oxidation is happening then it is an anode ??

please correct my every mistake ..!!

[mjc123]

Yes. The cathode is always the electrode where reduction occurs, and the anode is the electrode where oxidation occurs.
In a galvanic cell, a spontaneous chemical reaction gives rise to an electric current when connected. The reduction reaction at the cathode consumes electrons, making it positively charged, while the oxidation reaction at the anode releases electrons, making it negatively charged, so electrons flow through the external circuit from anode to cathode.
In an electrolytic cell, passage of electric current causes a non-spontaneous chemical reaction to occur. Electrons have to be pushed into the cathode to effect the reduction, and pulled out of the anode to effect the oxidation. Hence the cathode is the negative electrode, and the anode the positive electrode, while in a battery the cathode is the positive electrode. But in each case the cathode is where reduction happens - that's the important thing.