Okay.
Overseas, fabric softeners are commonly referred to in ENGLISH as "fabric conditioners". You see this in England, Australia, etc.
If you go to a traditonal, American, big-name supermarket in the New York City area, and buy a product such as Suavitel, whose identity has roots overseas, it is most likely to be not a concentrated version, but a 64-ounce bottle with bilingual labelling (example "Acondicionador de Telas/Fabric Conditioner")...this product may be a bit thinner than, let's say American Downy or Gain Fabric Softener, but, to me, is still essentially a fabric SOFTENER in the mainland sense.
Now, if you go to the dollar store, you'll notice much smaller-sized bottles of Downy, Suavitel, and sometimes other unfamiliar brands. These products have a somewhat different texture, not necessarily thicker or more powerful, but generally a MUCH more powerful or different fragrance added to it.
These products are almost always exclusively labelled in Spanish only, because they are targeted by the corporations that manufacture them DIRECTLY to the Spanish-speaking populations that favor them in the US, AS WELL AS Spanish-speaking populations in Spanish-speaking populations in Mexico, PR, etc. (the Dominican community generally use other products)....
If a bottle's label is exclusively in Spanish, and it has a label stating "Made in USA", it may also have been produced in Puerto Rico. It may also have a message on it that says something to effect of "(not) for use in the Continental United States" or something, but we still see them.
I have found (and heard from other launderers) that the dollar-store products have a higher rate of reactivity from individuals who use them then the US supermarket varieties that have bilingual labels. I used the small-bottle, dollar store Downy that has an extreme floral fragrance--nothing like the "ultra Downy" or, for old-schoolers, "Downy TC" (triple concentrated) formulas--for many years, despite the messy, drippy, old-fashioned pink cap, and consistently broke out and was irritated more frequently....I have tried the miniature white Snuggle "baby" formula in the dollar store...and STILL react skin-wise to it.
This is not a cost savings long term. In my opinion, it's not worth it.
If you have an A&P, Waldbaum's, or Food Emporium near you, check out their America's Choice FABRIC RINSE, which differs from America's Choice Fabric SOFTENER. It comes in a big, light-blue, bleach-bottle shaped container with a plain white cap. It will be marked "Made In Canada" and is made (I think) by Colgate-Palmolive and closely resembles the Canadian "Fleecy" brand.
It is much less expensive, is VERY lightly-scented and dyed, very light-blue, and leaves a decent degree of softness without the waxy heaviness that (I believe) causes a lot of skin sensitivity.
I have tested and found that the supermarket-brand (never Solo or Xtra, etc.) knockoff of Downy Regular Concentration softener and even the least-expensive pink fabric softeners are less irritating. I have no idea why, except for my waxy theory and the fact that, when you let these corporations start THINKING they know what we want, they never give us what we need.....
You can try the white-bottle Downy Sensitive concentrate with no fragrance, but odds are that won't go over big with your parents, who probably expect to see SOME fragrance and color in their softener.....it is also fairly expensive.
Bottom line? The fragrance and consistency of the CONTENTS of the bottle are far more important than whether they call it conditioner, "acondicionador", softener, or rinse. Also, everyone's skin is different.
Try using half as much fabric softener in the final rinse, and replace the difference with an equivalent amount of white vinegar. This does something to the final rinse--cheaply--that makes clothes less irritating and is okay to mix with fabric softener. Any leftover vinegar smell vanishes as the clothes dry.
Do NOT add fabric softener in with the detergent for the wash cycle, thinking the extra rinse will do it good. It cancels out the cleaning powder of the detergent, cause shmutzy buildup on your clothes, and undermine the good health of the innards of your machine!