Jupiter, and what it is actually said to do
Sagittarius answers to Jupiter, which classical practice calls the greater benefic and treats as the principle of expansion. Jupiter takes about twelve years to circle the zodiac, spending roughly a year in each sign, so it is a generational marker as much as a personal one: everyone born within a year of you shares it.
That has an awkward consequence for compatibility writing. The planet said to define the sign is the one that varies least between people of similar age, which means the Sagittarius ruler is doing far less to distinguish individuals than Mars or the Moon, neither of which appears on any shortlist.
The four names and their origin
Aries and Leo are the remaining fire signs, each a third of the wheel from Sagittarius. Aquarius and Libra are air, a sixth of the wheel away. Old practice grades those two separations as easy and the sign names are simply what stands at them.
The list is therefore a geometrical fact restated in personal language. Nobody assembled a set of Sagittarius partnerships and noticed that the fire ones held; the angle was ruled favourable first and the names supplied afterwards.
Mutable fire against the recommended four
Sagittarius closes its season, which makes it the adaptable member of the fire group: it will change route without much argument, but not destination. Against cardinal Aries the traditional reading is two people starting things, one of whom will follow through. Against fixed Leo it is enthusiasm meeting a requirement that the enthusiasm be sustained. Against Aquarius and Libra it is conviction meeting people who like to examine it.
These are sketches of category behaviour. They describe a plausible division of labour and predict nothing about two named individuals, which is the limit of what sign-to-sign reading can do.
Where the real information lives
The sun is one entry in a chart that runs to dozens of them. A comparison worth conducting reads both Moons for what each person quietly needs, both Venus placements for how affection is offered and recognised, both Mars placements for the shape a disagreement takes, and both ascendants for what each shows on first meeting. Then it measures the aspects that run from one chart into the other, which is synastry. The synastry calculator does this from two birth times.
None of it will produce a soulmate. Nothing in the technical vocabulary corresponds to the word, and the classical authors never attempt to locate such a person.
A better question to put to a pair page
Read the combination you are actually thinking about, listed or not. Sagittarius and Virgo, a square between two mutable signs, will teach you more than Sagittarius and Aries, because it has to explain how two adaptable people manage to keep missing each other.
With both birth times to hand, compare the charts themselves. That question is narrower than the one people bring and it has a real answer.
Questions people ask about this
Which signs does tradition pair with Sagittarius?
Aries and Leo in fire, Aquarius and Libra in air. All four are consequences of the two angles classical practice reads as favourable.
Can a chart comparison find a soulmate?
No. There is no placement or aspect for it and the older sources make no such claim.
Why is Jupiter less useful than it sounds?
Jupiter spends about a year in each sign, so everyone of a similar age shares it, and it distinguishes individuals poorly.
What should be compared instead?
Moon, Venus, Mars and ascendant in both charts, and the aspects running between the two.