This constantly comes up.
There are two different things that are both called STABILIZED.
One is wood that has been completely dried to around 7% moisture content, then totally impregnated with a resin ( usually acrylic), and then goes through polymerization of that resin ( the curing process) . This fills the wood fibers with resin inside and out, preventing moisture absorption and the swelling and shrinking caused by it. It also makes the wood capable of attaining a high polish with nothing but sanding and buffing, and can make unusable woods with great figure and spalt usable as high end handle material. The resins and process are both expensive, and while some make a system to do it at home, this is really the realm of the pros and big equipment. WSSI is the champ on stabilization,IMHO. This process ,makes the wood pretty resistant to absorbing water,blood,grease and oil, food juices, etc.
Slightly related to this process is the use of things like Minwax wood hardener and curing oil finishes ( Polyacrylic,tung,walnut, Danish etc.). This helps the surface a bit, but is not nearly the same penetration as above. The NorthCoastKnives tutorial is this type of process.
The other thing called stabilization by some, is a term used by wood workers and wood turners. It involves soaking the green or high moisture content wood in one of many solutions that will penetrate the wood surface to some degree, and thus slow down drying to limit checking and splitting. With systems using pressure and time, some of these chemicals will penetrate the wood very deeply. The big difference is that they just don't do anything to make the wood stronger or much more stable...just slow drying. Eventually many of these will evaporate, leaving the wood dry. That is fine for a bowl or vase, but on a knife handle the now dry wood can still absorb moisture,blood, and fish juice, as well as swell and shrink. Pentacryl, Nelsonite, and several other brand names are the normal ones used. Some smell like solvent. A Nelsonite soaked handle can retain the smell for many years.
The biggest problem often comes in buying wood from an online seller with the wood labeled as "Stabilized". It can often look good, but performance and durability can be vastly different. Ask the exact process used, and if they are not forthcoming with clear answers, or claim it is a secret, then it is probably best to pass on that wood.
The other way to recognize one from the other is price. If the wood is labeled as "Stabilized", but is $5-10 a block, chances are it was not done by WSSI. Always get a return guarantee from the seller, and if the wood feels too soft, or looks too dull, send it back.
All that said, there are those who absolutely hate the look and feel of acrylic stabilized wood. They like the natural look , and thus use unstabilized wood, or wood done by one of the other processes. These handles will usually need a finish coating of some sort.
Hope this helps sort it out.
My advise has always been.....You should send wood that needs stabilizing to WSSI.
Stacy