FWIW, personally, I don't see as sharp a demarcation as some on the terms "dino" vs. "synthetic". The Group category is much more straightforward for me. JM2C.
For final use all contain a blend of molecule sizes as part of the blending process, much like fuels such as gasoline, diesel, and heavy fuel oil contain boiling ranges of molecules as opposed to high purity propane for example. But the ranges of molecule sizes and structures in lubricants are generally more narrow than in fuels.
Group I typically only uses solvents to extract molecules that are less desirable as lubricants from a specific boiling range of molecules distilled from crude oil base, leaving a mixture of molecules with more desirable lubricating properties behind. No real chemical reaction is involved, just selective boiling & condensation (distillation) and solvent extraction.
Group II adds reacting the molecules with desirable lubricating properties with hydrogen to remove by chemical reaction conversion more undesirable atoms & molecules to produce stocks with better stability with respect to temperature, oxygen, etc. This might be performed on both virgin distilled fractions of crude oil as well as certain cracked stocks from fluid catalytic cracking for example where even larger molecules were first distilled then broken up molecularly then again distilled into different "cuts" - gasoline, heavy distillate, etc. A wider range of crude oils can be used to produce the molecules with desirable lubricating properties than simple distillation and solvent extraction. Chevron even defines the 'unofficial' Group II+ stocks, at least with their definition.
http://www.chevronbaseoils.com/faq.aspx
http://www.motivalubes.com/FAQ.htm
Group III in general is selectively making something smaller from bigger molecular building blocks that originally came out from underground. This is an even higher degree of chemical reaction and molecular manipulation than Group II. A much wider range of crude oils can be used for this process. Hydrocracking and maybe fluid catalytic cracking prior to hydrocracking are generally involved. This includes ExxonMobil Visom as well as others. I see some use a GroupIII+ designation (Visom) but this is an 'unofficial' designation
http://www.exxonmobil.com/UK-English/Basestocks/PDS/GLXXENBSKEMVisom.aspx
GTL is building something bigger from smaller molecular building blocks that came out from underground, but can involve selectively breaking the larger building blocks (cracking) as well to obtain the desired molecule size range (i.e. cracking of slack wax that was built up from methane molecules). As the carbon chains build, hydrogen is released from the molecules to make room for the increased carbon to carbon bonds. That same hydrogen (plus any additional required) will then be re-used in the cracking process to produce the series of desired molecule sizes. Shell named their process PurePlus Technology.
http://www.shell.com/global/future-energy/natural-gas/gtl/products.html
http://www.machinerylubrication.com/Read/422/gas-to-liquids
Group IV Polyalphaolefins (PAO) is building something bigger from smaller building blocks (oligimerization), but the smaller building blocks generally came from cracking larger building blocks that came out from underground (fluid catalytic cracking and / or steam cracking is typically used to produce the ethylene from petroleum, although some ethane from natural gas liquids that came from underground is dehydrogenated to make ethylene). For ExxonMobil, oligimerization is eventually followed by selective hydrogenation. ExxonMobil and Ineos are the largest producers. ChevronPhillips is also a significant producer of PAO.
http://utsrus.com/documents/seminary_doklady/exxon_mobil_pao.pdf
http://www.ihs.com/products/chemical/technology/pep/reviews/exxonmobils-ultra-high-viscosity.aspx
http://www.cpchem.com/bl/pao/en-us/Pages/default.aspx
Group V is a catch-all for everything that doesn't fit in the other groups. I worked as an engineer at a refinery that produces pale oils from crude oil that comes out of the ground in a separate set of units from the main refinery that produced typical fuels. The Green Earth Technologies bio-based oil is also classified as Group V. So Group 5 can include stuff that came from underground after cooking as a stew for millions of years as well as stuff grown just this year. Think of Group V as "None Of The Above".
http://www.getg.com/G-OIL_motor_oils.php
http://www.getg.com/G-OIL/bio-based_advanced_full_synthetic_motor_oil.php
Oils in every one of these groups endure some form of separation process, such as distillation, sometimes before, sometimes after, sometimes before & after being consolidated into the desired process stream. There are degrees of 'uniformity' in all of them.
Hope this helps. Kinda long-winded but as with many things it's not as simple as it seems on the surface.