The "art" of making fasteners stay where you put them is considerably more complex than is comprehended by most people - and that includes lots of rather excellent mechanics and experienced assembly line people.

There are a few hundred different standards for bolts/screws and nuts for "simple" fastening. There are at least half as many for "retaining devices" that are separate parts to be added.

Mention was made above that a main difference between Whitworth standard threads and SAE is just the thread angle (properly called the flank angle). The difference between 55 degrees and 60 degrees may seem small, but the 55 degree flank applies more radial force, tending to expand the female half of the joint, than the 60 degree, for the same bolt tension. This is one reason that US standards more generally permit retention devices like "prevailing torque nuts" - a.k.a. locknuts, spring lockwashers of four or five common kinds, and even "adhesive retaining compounds" (Loctite). UK Aircraft standards don't permit any of those in most places, partly because when the Whitworth threads were almost universally used, you'd split the nut before developing full tension in the bolt and the Brits' nuts fell off a lot.

On airplanes designed to UK regulations, after EVERY NUT is screwed on and tensioned, you MUST drill a hole through the nut and bolt, and install a cotter pin, or in less critical cases or where there isn't a separate nut, you must use a lock wire (unless the regs have changed recently, which is unlikely).

Spring washers, of the common kind, only retain loose nuts. The "spring" is fully compressed at a bolt tension well below what is required to keep the bolt from loosening in the presence of vibration. It may keep the nut from falling off quite as quickly once it comes loose, but is worhtless for maintaining tension at the 80% of fastener yield stress commonly applied for secure fastening. You use them where the screw would be "inconveniently small" if sized for the clamping needed, and the screw that's "really too big" might break what it's screwed into if you tightened it enough to keep it in.

In cases where the male thread goes into a housing rather than having a nut, the spring washers also can cause sufficient damage to the housing to require replacing the expensive part after very few repairs/adjustments.

The Brit drilled-in pin method nearly always requires replacing both screw and nut even in simple joints every time an adjustment is needed. Of course that's still cost effective compared to replacing a pump or motor.

There are specific US regulations, varying between agencies, for how many times a prevailing torque fastener can be re-used, and in some cases specific inspections that are necessary for any re-use. Some screws/bolts are re-usable a half-dozen times on aircraft if they pass the inspections each time, but "locknuts" almost never get past three-times-on.

You should be able to rely on the manufacturer to have decided what kind of fasteners are needed in a particular product; and to the extent that you can assume competence there, using the "same" fastener for a repair is highly recommended. With the multiplicity of fastener variants available, knowing what is a "form-fit-and-function replacement" really is a bit much to expect of the general population, so getting an "original replacement" part from the original source is still recommended if there's any uncertainty.

Learning to assess what fasteners (and alternates) you should use for a particular application does take some study. It's not too hard to find the information necessary to match a broken fastener; but only of few (like me, and that one other person here whose name I can't recall, of course) have time to learn it all for a problem that only comes up occasionally.

I did pass over mentioning that Home Depot in my area does have limited selections of Grade 3 fasteners, and sometimes a few Grade 5; but both selection and price are generally better at O' Reilly's or Autozone (as examples only). If there's one in your area, Tractor Supply is also sometimes a good place to look for larger sizes of "machine quality" parts like fasteners.

If the part you need to replace hasn't been lost in the weeds, taking the old part with you to the hardware guys often can get you a proper enough replacement since all "graded" fasteners are generally marked to indicate exactly what they are.

John