the magnetic field of a magnet forms two half spiral that comes out from the N to the S but an electron's was a spiral that warps around itself, Why are there field lines different? Shouldn't they be the same since a magnet's field lines is basically made of electrons facing the same way?

Some people don't draw the magnetic field lines that are within the magnet, but as you suggested, they are there. The only real difference would be a slight distortion since for example the magnet can be longer.

if I want to visualize the magnetic field of a moving electron, can I say that it is the same as pushing a stick magnet (horizontally) across?

Well, electrons have an intrinsic magnetic moment. The magnetic field generated by a moving electron (rather than its intrinsic one) will look very different -- I think it was circles perpendicular to the motion of the electron, with their density falling off as 1/r^2. If you move several electrons in a circle, you again get a magnetic field similar to that of a magnet.

I'm sorry but I'm not sure what you're saying. Maby I had visualize the magnetic field of an electron wrong.

So to make sure if I'm on the right track where is the north and south pole on a moving current?

I'm sorry but I'm not sure what you're saying. Maby I had visualize the magnetic field of an electron wrong.

So to make sure if I'm on the right track where is the north and south pole on a moving current?

 

It's circular about the wire. The field direction is given by the right-hand rule: If your thumb points in the direction of the conventional current, your fingers will curl in the direction of the field.

I'm sorry but I'm not sure what you're saying. Maby I had visualize the magnetic field of an electron wrong.

So to make sure if I'm on the right track where is the north and south pole on a moving current?

 

The intrinsic magnetic field of an electron is different than the magnetic field of a current. The electron is like a tiny tiny magnet.

 

The magnetic field of a current is circular around and perpendicular to the wire as swansont said, so that it doesn't have any pole. However, if your current is a loop some of the magnetic field cancels out and it ends up with a magnetic field like a magnet's with the poles perpendicular through the center of the loop.

 

Magnets don't really have poles, we just pretend they do. But you can't separate one of these "poles" from the other.