Rodney, both are wire feed arc welders, one is mig, using steel wire and gas, say co2 and argon, this is for a shield during the actual weld to keep impurities of the molten weld, it's a gas shield, that is for Mig. The flux core is also a wire feed arc welder, however, it does not use gas for shielding, but has flux in the center of the wire, thus named flux core wire welding, it's size is .030 and .035, Mig wires are usually .023, .025 or .030.
The mig produces nicer, cleaner and more nice looking welds, the flux core is rougher and the welds are not as nice,the flux has to be wire brushed off after the welds, they produce more heat, so light gauge tin it will burn through easily. On old mopars with 16 and 18 gauge tin, I had no problems welding with flux core, although I did burn through at times. When you buy your welder,many smaller machines, the hobbyist/home use type can use either wire, some are strictly for flux core and some can be converted to mig use. The choice is yours and whatever your pocket book and future use of the welder dictates. All the best from The Rock of the North