You are correct in discerning some subtle differences between the polishes. Depending on the color, the Sephora colors can be thinner or thicker than the OPI colors. My newer OPI colors have a different feel from the original ones I bought as well as different opacity. If you look at the ingredients, they are the same for the Sally Hansen, OPI, and SOPI gels. There are two LED lamps sold by Sally Hansen: one for their gel polish and one to be used with their Insta Gel kits. The Salon Pro Gel lamp lists the same 30 second cure time as the SOPI lamp. They are the same shape, have the same style wall cord, and the same LED lights, but are different colors. Also, the cost per ounce of the polishes is about the same: Sally Hansen is $11.99 for 1/8 ounce. SOPI is $17.95 for 1/4 ounce. OPI lists its gels at $34.00 per 1/2 ounce -- although it can be found for much, much lower prices. Broken down to a per ounce price, the Sally Hansen colors are the most expensive! All three formulations need to be well shaken before use. The biggest differences are in the packaging and brushes, which is a function of branding. Btw, I find that the IBD Just Gel polishes are similar to the OPI polishes in texture and use as well, but I haven't had any staining or shrinkage problems with IBD, which I have had with certain OPI colors.
I suspect that there aren't many places making gel polishes and that all of the gels originate in the same few facilities. So far, there seem to be three main differences in formulation: whether the polish needs to be shaken; whether it is LED/UV light curable; whether it is only UV (fluorescent bulb) curable.
All the lamps are made in China, and are all very similar as well. Curing times also seem the same, only differing by the power of the lamp. The Red Carpet Professional lamp uses a 45 second cycle, which is the same as the Gelish Mini Pro 45 Lamp. From personal experience, I know it cures OPI and IBD Just Gel as well. The Gelish 18G lamp has the same cure times for the gel colors as the OPI professional lamp. Gelish Foundation and Top It Off cure more rapidly using that lamp, but they list faster cure times for other lamps as well. The biggest difference I have found is whether it cures the whole hand or just four fingers. That is a function of design and size, not power.