To shed a little more light on the subject: VAR (vacuum arc remelting) is a refining process used when conventional air melted or vacuum induction melted metals do not meet cleanliness standards for demanding applications (typically aerospace).
Essentially, an air melted or vacuum induction melted "consumable electrode" is cast in the same manner as a traditional ingot. The electrode can be bottom-poured or top-poured. The electrode is then conditioned (surface ground) and a stem welded to the top end. The stem allows the VAR furnace to hold and control the arc gap, and also provides a connection to the electrode to pass the remelting current through. The electrode is then placed in a water-cooled copper crucible and the whole set-up is then sealed and pumped down (usually to 100-300 microns). An arc is struck (ind. standard is 24V) between the electrode and the crucible bottom and a melt pool is formed. Upon establishing a stable arc and melt pool, the electrode is lowered (using computer-controlled motors) and the arc gap is maintained. Think of it as "stick welding", with a 5 to 15 TON stick. As the arc melts the electrode, droplets of the molten metal fall into the melt pool, and non-metallic inclusions float on the molten metal. Also, any entrapped gas in the electrode is removed, and some lower melting point alloy metals are volatilized.
Although this is a generally viewed as a way of "cleaning up" the metal, VAR does not always remove all non-metallic inclusions. If there are any arc disturbances during remelt (usually caused by outgassing), this can upset the melt pool, and cause localized solidification, which may lead to entrapment of large non-mets, which will cause cracking in subsequent processing of the ingot.
VAR also provides a microstructure that is typically better than conventionally cast ingots. By far the most common VAR steel is 15-5 stainless. VAR is also the preferred refining process for nickel-based superalloys.
ESR, or electroslag remelting, uses an electrically conductive slag through which the arc is struck and molten metal drops through. The welding analogy for this is SAW, submerged arc welding. In ESR only the large oxides in the electrode float out. Very, VERY fine non-metallics still get entrapped in the metal, but they are EXTREMEMLY small, and are usually evenly distributed throughout the ESR ingot, with no adverse effects on workability or physical properties. In ESR, the slag stabilizes the arc and the melt pool, and is not nearly as sensitive to outgassing as VAR.
The VAR or ESR ingot is then hot-worked like a traditionally cast ingot.
On a side note, US aerospace manufacturers typically specify VAR over ESR, although the rest of the world prefers ESR over VAR. VAR is a very delicate balancing act between arc voltage/current, melt rate (arc gap), and vacuum level, all of which are easily upset by poor electrode surface and internal quality.