Saving throw names are a biproduct of the very traditional dungeon crawling environment they were built for. As such, their names can seem awkward and difficult to assign to certain effects and traps.

The first thing to understand when determining what type of save should be given to the effect you are designing is to first consider if it should be a save at all.

If it's a trap, don't shy away from giving it a THAC0 instead and having it make an attack roll. AC already represents a characters ability to avoid harm, so why add further complexity. This should be the default design you use it the attack's intent is simply directly to cause harm and little else (for example, arrow traps)

If it's something that armour and dexterity aren't going to be as effective against, then you move on to figuring out the appropriate saving throw.

The first thing to know is that the saving throws are listed in an order from 'generally easiest to pass' to 'generally hardest to pass'. They are as follows.

  1. Death, poison
  2. Wands
  3. Paralysis, petrification
  4. Breath attacks
  5. Spells, rods, staves

You should assign an effect to the first category that fits.

Death should be given to things which have a high chance to instantly kill or inflict poison or other malicious bodily status effects. These saves are the easiest because of their lethality.

Wands should be given to any effect that requires a physical implement being aimed at the target. These saves are the second most easy because they telegraph themselves heavily in the fiction due to a device being pointed towards the target.

Paralysis and petrification should be given to any effect which alters or impedes a persons movement, such as pushing or shoving them, as well as more magical effects such as gorgon petrification, it is often assigned to falling rock traps under the idea of 'pinning someone under the rock'. These are the middle ground of saves as there is often not an obvious telegraph that can be avoided, or if there is it has enough momentum to physically displace a hardy adventurer and so is not easily dodgable.

Breath attacks applies primarily to the lethality of dragon breath, but can also be applied to any other elemental effect which attempts to fill a room or large space. These effects are difficult to avoid due to their huge effective areas.

Finally, spells, rods, and staves. This should be assigned to any effect that requires little more than a device activating (but not being aimed), or a mage whispering an encantation under their breath. It's not obvious who the target is, or what the effect will be, until it happens, making them the hardest of all saves.

If you make it to the end of this list without having concluded which saving throw is most appropriate. Make it a death save because saying "save verus death" is always going to scare players, even though it's the easist save to pass. You might find this trivialises your very inventive trap, but if you've come up with something so complex that it doesn't fit into one of the above categories, and you don't already know what you are doing well enough to figure out a saving throw for it, you should probably consider swapping it out for something simpler to begin with.

The next obvious question is to ask what form the successful saving throw takes in the fiction. Sadly, B/X offers little advice on this front. Fortunately, the holy grail of OSR advice comes to our rescue in the form of the AD&D 1e Dungeon Masters Guide. It has this to say.

The term saving throw is common enough, coming to us from miniature wargames and D&D. It represents the chance for the figure concerned to avoid (or at least partially avoid) the cruel results of fate. In AD&D it is the same. By means of skill, luck, magical protections, quirks of fate and the aid of supernatural powers, the character making his or her saving throw takes none or only part of the indicated results—fireball damage, poisoning, being turned to stone, or whatever.

Someone once sharply criticized the concept of the saving throw as ridiculous. Could a man chained to a rock, they asked, save himself from the blast of a red dragon's breath? Why not?, I replied. If you accept fire- breathing dragons, why doubt the chance to reduce the damage sustained from such a creature's attack? Imagine that the figure, at the last moment, of course, manages to drop beneath the licking flames, or finds a crevice in which to shield his or her body, or succeeds in finding a way to be free of the fetters. Why not? The mechanics of combat or the  details of the injury caused by some horrible weapon are not the key to heroic fantasy and adventure games. It is the character, how he or  she becomes involved in the combat, how he or she somehow escapes—or fails to escape—the mortal threat which is  important to the  enjoyment and longevity of the game.

A character under magical attack is in a stress situation, and his or her own will force reacts instinctively to protect the character by slightly altering the effects of the magical assault. This protection takes a slightly different form for each class of character. Magic-users understand spells, even on an unconscious level, and are able to slightly tamper with one so as to render it ineffective. Fighters withstand them through sheer defiance, while clerics create a small  island of faith. Thieves find they are able to avoid a spell's full effects by quickness...

~ AD&D 1e DMG, "Combat (Saving Throws)"

I don't think I am capable of giving better advice for resolving the fiction than is given there in the AD&D 1e DMG. It is not the type of the save that determines the form it takes, but the nature of ther person making it.