Aditya, they are not the same. There is no such thing as a bar magnet whose magnetic moment is due to electric currents alone. A bar magnet is composed of a ferromagnetic material such as iron and its magnetism is mainly due to electron spins (spin is a fundamental quantum property and there is no evidence that it involves any actual motion). The orbit of each electron also contributes to the magnetic moment of an atom or ion, but in the transition metals (which include iron) it is quenched and is small enough to ignore. There can be "eddy" currents in magnetic metals and alloys, but they contribute little to the magnetism. Thus, a bar magnet is quite different from an electromagnet, and its magnetism is due to electron spins, not electric currents.
Spins of electrons in neighboring atoms are aligned by the exchange interaction, which is a consequence of the Pauli exclusion principle. This ordering can give rise to ferromagnetism as long as the temperature is not too high.
For more information, see Chapter 15 of Kittel, "Introduction to Solid State Physics", 6th ed., John Wiley & Sons 1986; Chikazumi, "Physics of Ferromagnetism", 2nd ed., Oxford, 1997; and Spaldin, "Magnetic Materials: Fundamentals and Applications", 2nd ed., Cambridge, 2011.