There is a tension formula here somewhere where you can take the tension of the string you are using and the difference in pitch you wish to achieve, and you can determine what the resulting tension will be. Hopefully someone will come along and mention it or how it works, because I always found it confusing. I think "it depends" is the best answer I can give. For example 4/4 Spirocores come in a C and and H, that have different product numbers. The C comes in a weich and mittel, where the H comes in mittel and stark. The mittel H has the same tension as the mittel C, so it could likely be used as a Stark C if you tune it up the semitone. 3/4 only come as a weich and mittel C and a mittel H. They also have weich and mittel C's for the Red Mitchell 5ths set in 4/4 and 3/4, which have different tensions again. That's 11 bottom strings if you gave up counting, all of which are a different combination of tension and intended string length, which likely also involves a difference in gauge.
If you like a Spirocore on the bottom, you've got options. If you like something else down there, you may or may not have options. Some of Thomastik-Infeld's other offerings only come in a C or H, and/or don't have different tension options. Other companies are left to their own devices as well.
As a guy in 5ths, I have encountered a few of the lesser known companies that offer a "5ths set" that is made up of a solo A, orchestral D, solo F#, low B/C and they don't even repackage them to try to trick you into thinking they were specifically designed for 5ths. If you stick with the big guys like Pirastro and Thomastik-Infeld, you can be pretty sure they are different strings. If you look through Pirastro's strings, they offer a low B and a solo low C# for some of them, and some of the low B's come in Dunn, Mittel, and Stark tension as well.
Personally, I have used the Spirocore 4ths weich low C (I'm assuming 3/4 as that is the most common in Canada but it's been a while and I don't recall specifically) and the Red Mitchell 3/4 weich and mittel low C's. I tune them to a C, although I have experimented with going down to B or Bb on occasion. the 4ths weich and RM mittel are pretty similar in tension 30.0 and 30.6 kg respectively, but I don't have the two of them to compare for gauge if they are different. The RM weich is 27.5 kg, and was a wet noodle on my bass. I am currently playing the RM mittel and very happy with it. My bass has a 41.5" string length which could make a difference if your instrument is dramatically longer. I have also used a Bel Canto low H tuned up that felt quite nice, but after the break in period it got darker sounding and I couldn't hear pitch very well on it. I played the Velvet Compas 180 V's set for a while that is no longer in production, the old Obligato 5ths C before they changed it, and a Corelli that was unremarkable but I don't know which one it was and all of those things are not helpful anyway.
There is a difference. You just have to find the right one for your particular instrument and taste.
