@Kissing, tension for steel string guitars depends on scale AND on string gauge. Many people would not put medium or heavy gauge strings on a small guitar because tension might be too high and destroy guitar. And extra light strings on big guitar often sounds too thin. For ukulele things get more complicated because different string materials have different density. For example fluorocarbon strings have higher density so same tension can be accomplished with thinner string than nylon string on the same scale.
Again disagree here.
From the perspective of achieving a certain level of string tension:
Medium/heavy gauge
should be used on smaller guitars because shorter scale means the tension is less when tuned up.
Lighter gauge
should be used on longer guitars because longer scale means the tension is more when tuned up.
Unless the guitar is intentionally made weaker, there is no inherent reason why a small guitar is structurally weaker than a large guitar.
Size does not = structural strength. A guitar maker may
choose to build a small guitar with lighter construction, but they can just as easily build a small guitar that is heavily built.
Generally speaking, in order to reach that "sweet spot" tension on guitars I would install heavier strings on shorter guitars and lighter strings on longer guitars. Of course, it all depends on the type of guitar, the setup and what kind of sound I am going for. The choice of avoiding "lighter" tension strings on longer guitars is a matter of your preference and choice of guitar. Installing light strings on a large guitar does not necessarily mean you get a thin sound. It means you will have a big sound due to the size of the guitar at a particular string tension. Of course, medium or heavier strings would create a bigger sound, but at the cost of increased tension.
Furthermore, you may want heavier strings on a small guitar to produce a large sound as possible on a small body, as well as adjusting for the reduced tension caused by shorter scale.
However, since the guitar industry does not release their strings under arbitrary names like "Soprano concert and tenor" the player can use the above concepts to make a decision on what strings would go well with their particular guitar.
The same applies on nylon strings.
If I wanted to tune a 3/4 or 1/2 size classical guitar to the same tuning as a full size 4/4 classical guitar, I would opt to use heavier gauge strings not lighter.
You can install tenor ukulele strings on concert and soprano ukuleles. It will just result in a different tension compared to what you would on the same company's concert or soprano set.
With ukulele it gets a little interesting too.
It seems manufacturers consider tenors to inherently have harder tension than sopranos and concerts.
Therefore, they manufacture tenor strings to be thicker gauge and therefore harder tension.
However, if we were to view soprano, concert and tenor ukuleles as "short scale ukulele" and "longer scale ukulele" like we did with the guitar example above, you would actually be installing heavier gauge strings on sopranos and lighter gauge on tenors.
This is precisely the reason I prefer installing concert strings on tenor ukuleles.
Most tenor strings have more tension than I prefer.
Concert ukulele string tensions, if we are to go by D'addario, correspond to regular classical guitar strings (4th to 1st) and Tenor ukulele string tensions correspond to hard classical guitar strings. This is actually a bit counter-intuitive, as you are further exaggerating the harder tension on tenors caused by the longer scale by giving it heavier strings. So you end up with an instrument with exponentially (figuratively speaking) harder tension compared to a soprano or concert using lighter tension strings (which further exaggerate the lighter tension caused inherently by the shorter scale length).
The goal, whether it be Ukulele or Guitar, is not to put heavier strings on longer instruments and lighter strings on shorter instruments. The goal is to achieve a certain user-preferred level of tension at a given tuning on a certain scale length. As a general rule, the tension is less on a shorter instrument for the same tuning using the same strings compared to a longer instrument.
By that logic, one should actually be installing heavier strings on a Soprano uke and lighter strings on a Tenor uke to meet in a certain 'middle ground' of tension.
As for your comment on choice of materials (eg: fluorocarbon), it's actually not complicated for us because the string companies have already done the difficult part of working out what gauges and densities are suitable for the ukulele. All we need to do is pick and choose, since the string company have already named the strings as "soprano concert tenor" (i.e. already worked out equivalent working tensions compared to conventional nylon strings).