Why bar magnet can produce magnetic field? Say I wrapped a piece of wire around an iron bar in a closed circuit connected to a DC power supply, the electrons starts flowing and moving charge produce magnetic field. Yet a bar magnet can produce a magnetic field without any charged particles moving around, are the magnetic fields produced by the two objects different types?
 A: All macroscopic objects we observe are emergent from the underlying particle/atomic/molecular nature, which by the way follows quantum mechanical equations.
a) The reason we see electric fields is fundamentally because electrons and protons have electric charge, which generates their electric field. There are many ways that electric fields can be macroscopically induced. Analogously, the reason we see magnetic fields is because particles/atoms/molecules have magnetic dipole moments inherent in their nature, which have elementary magnetic fields.
b) A second source of electric and magnetic fields comes  from the behavior of elementary  and fields under motion:  they obey Maxwell's equations, which tell us that changing electric fields generate magnetic fields and changing magnetic fields generate electric fields.

Say I wrapped a piece of wire around an iron bar in a closed circuit connected to a DC power supply, the electrons starts flowing and moving charge produce magnetic field.

A magnetic field is generated from the moving charges due to the laws of b), and the small dipole ferromagnetic domains  described in a)  orient themselves according to the external field and magnetism is retained even when the current is off. The current enhances the total magnetic field after first orientations of the dipoles.

Yet a bar magnet can produce a magnetic field without any charged particles moving around, are the magnetic fields produced by the two objects different types?

In a permanent magnet the domains after being oriented in a direction retain it because they are in the lowest energy state of the solid when oriented. 
The magnetic field is the same type of  field for all cases.
A: There is only one type of magnetic field, but there are multiple ways to generate a magnetic field. A bar magnet has a permanent magnetic field while a electromagnetic has a magnetic field only when the current is applied. 
Another way to get a magnetic field is to induce one. So you place an iron bar near one pole of a bar magnet but not touching. The bar magnet will then induce a magnetic field on the previous nonmagnetic iron bar.  
For superconductors you can float a magnet over them. The magnet induces an electrical current in the superconductor which creates a magnetic field within the superconductor. The magnetic field in the superconductor is opposite the magnet so the magnet floats over the superconductor (Youtube video).  
