Gelling can give a more translucent look to the soap (see soaps by
@dibbles - some of her soaps are almost ethereal in the way they look!), and are easier to get a shine on the finished soap, with a smoother, sometimes waxier, look to the final soap.
Ungelled soaps are more opaque and pastel hued, with a creamy look to them.
If you want to watch gel in action, pour a small quantity of batter into a ziploc plastic bag and steam it gently ... you can see the change in the batter from creamy looking, to a darker, clear liquid ... it's that dark liquid phase that is the gelling soap. In a slab or log mold, you can sometimes see that dark gel, all the way to the surface of the soap. If the soap gets hot (you can feel it's hot just by holding your hand over the top or to the side), but you aren't seeing the dark all the way to the edge, just a little more insulation is needed next time, to avoid partical gel. Partial gel is a ring in the middle, of gelled soap, where the gel phase hasn't reached all the way to the edges of the soap).
I don't refrigerate my soap, so if I want an ungelled soap in my slab mold, I don't modify the recipe, I modify how I control the temperature in the final soap - if I want it kept cooler, I put it on a cooling rack and get some airflow around it. If the weather is hot, then I sometimes put the soap on ice (literally!) and run a fan over it.
Gelling is easier - if you use a lot of water, the soap will go into gel at a lower temperature. If you use less water, then insulating can retain enough heat to push the soap into gel. If that's not enough, then starting with warmer ingredients and insulating can help.
Gelling after the soap is in the mold can be done in the oven (that is CPOP), by heating the oven to just warm, then turning it off before the soap goes in. The residual heat acts like an electric blanket for soap - it keeps it warm enough to kick the soap over into gelling (and because the heat is both internally generated from the soap's exothermic reaction, and externally applied from the warmth of the oven, the gel can be quite even and complete. Overdoing the oven temperature can lead to rubbery soap
It is easier to stop soap from gelling if it is in smaller molds, and easier to help it gel as the mold gets larger (thermal mass plays a part).
Trivia: The amount of time the soap spends cooling (after gelling) can impact on crackle (or "glycerin rivers") in the soap - a slow cool allows more crackle to develop, and a fast cool "sets" the soap and minimizes crackle (so a CPOP soap left in the oven overnight is far more likely to have crackle than a gelled soap that has had it's insulation removed and been placed, still in the mold, on a cooling rack in front of a fan