In my created world, I struggled with the same issue. My experience is all 5E, no prior history or references at all.
Tieflings are descended from humans who had children with devils or made pacts with one of them (if there even is a difference)
Tieflings are derived from human bloodlines, and in the broadest possible sense, they still look human. However their infernal heritage has left a clear imprint on their appearance.
From the PHB. Stay with me here, because SCAG adds to it.
The Mark of Asmodeus
Subsequently, Asmodeus and a coven of warlocks, the Toril Thirteen, performed a rite wherein the archdevil claimed all tieflings as "descendants" of the Lord of the Nine Hells, regardless of their heritage, and changed them into creatures that resembled their supposed progenitor.
They can be descended from any of the nine (ten? Belial isn't mentioned in Mordenkainen's Tome of Foes as a tiefling subrace.) Archdukes or Archduchess of the Nine Hells. The nine varying subraces are on pages 21-23 of Mordenkainen's Tome of Foes. Asmodeus' subrace is the typical D&D subrace described in the PHB.
Cambions and Infernal Cambions are different things.
Cambion (Monster Manual)
A cambion is the offspring of a fiend (usually a succubus or incubus) and a humanoid (usually a human).
Spawn of Graz'zt. The demon lord Graz'zt is fond of procreating with humanoids who have made pacts with fiends, and he has sired many cambions who help him sow chaos across the multiverse.
Graz'zt is a demon lord who rules over The Triple Realm in the Abyss. And if you know anything of the Blood War demons and devils hate each other. So it sounds like Cambions can be any sort of creature that isn't a devil...
Infernal Cambions (MToF)
Some archdevils consort with mortals to produce cambion offspring. While most have the typical abilities for a cambion (as detailed in the Monster Manual), some gain abilities reminiscent of their archdevil parent.
It had to specify the difference. A typical cambion is a fiend's or demon's direct child, whereas a tiefling is a descendant of a humanoid race and an archdevil. None of the books exactly specify whether it has to be directly or not. It does imply that a tiefling's ancestry can skip generations or be direct.
Pg 62 Xanathar's Guide
1-4 Both parents were humans, their infernal heritage dormant until
you came along.
5-6 One parent was a tiefling and the other was a human.
7 One parent was a tiefling and the other was a devil.
8 One parent was a human and the other was a devil.5-6 One parent was a tiefling and the other was a human.
Cambions and Tieflings are not the same, but they are 'cousins.'
Let's look back to the cambion's description.
Cambions inherit aspects of both parents, but their horns, leathery wings, and sinewy tails are hallmarks of their otherworldly parentage.
Born to Be Bad. Cambions grow into ruthless adults whose wickedness and perversion horrifies even the most devoted mortal parent. Even as a youth, a cambion identifies its rightful place as an overlord of mortals. It might orchestrate uprisings in towns and cities, gathering gangs of humanoids and lesser devils to serve it.
Pawns of the Mighty. A cambion forced to serve its fiendish parent does so out of admiration and dread, but also with the expectation that it will one day rise to a place of prominence. Cambions raised in the Nine Hells serve as soldiers, envoys, and personal attendants to greater devils. In the Abyss, a cambion carries only as much authority as it can muster through sheer strength and force of will.
Tieflings seem to have more control in their lives and less pride in what they are. Now I can argue tieflings don't have wings but there are variations in the Sword Coast Adventurers Guide that are Feral, Winged, varying physical characteristics, and two new traits.
Cambions are direct lines that in my guess don't typically procreate after that with humanoids just due to the commonality of them and if they do - their fiendish, abyssal, or infernal ancestry would presumably get lost over time and cease to resurface. Although the inclination towards evil seems far stronger in them than their tiefling cousins. They presumably are counted 'blessed' and were sired by evil humanoid parents as well.
Tieflings are also direct lines although it seems to be more of a 'curse' that they are dealing with that was created from a pact struck generations ago or less commonly by their parent(s). I'd go so far to argue that they have stronger blood. If it can resurface later then I presume the infernal heritage is a much more powerful influence genetically (at least appearance wise) and that these children are more unintentional than cambions which seem to be intentional.
Alignment. Tieflings might not have an innate tendency toward evil, but many of them end up there. Evil or not, an independent nature inclines many tieflings toward a chaotic alignment.
So not the same as Born to Be Bad like the cambions.
Heck someone could argue that Cambions are what became Tieflings!
Keep in mind much of this is from the Forgotten Realms which was designed by Ed Greenwood, so if you are making your own world, play with it!
For my world, I decided that the gods, devils, and demons have left the inner planes, so tiefling's are all that's left. Cambions only existed before the gods disappeared. In my world, there are no humans, so my tieflings are Elven and Dwarven. It's your campaign: in the end, it's all up to you.