Yet, throughout the books, examples are given where Trigger is the activator for Potions. If you compare it to a gadget, say, an explosive, said explosive with a Trigger could be either a landmine (the type of trigger you mention), or a character waiting for certain circumstance and then said character 'pushes the button' to set off the explosives on purpose. Between this and the Potion Examples with Trigger, at least the way I read it, both uses are appropriate?
Trigger on a potion would affect the 'triggerer' (the person who drinks the potion).
With Trigger, by default you set a condition that triggers it. It can be "drinking the potion" or "stepping right here" or whatever, but that's what sets it off, and it defaults to affecting whatever triggers it. By spending more, you can vary the conditions, reset it at will, trigger it at will, and on and on. It's most often used for a self contained power, like a potion or a land mine, where the trigger is contained as part of the power. The Trigger condition has to be something that could be detected with the user's senses, so if it's based on a sense the user doesn't have, or isn't expected to have, you'll want to buy that Enhanced Sense (which you can buy with a Limitation: Only To Detect Trigger Conditions). Also, once a Trigger is set, it's no longer tied to the user; it's based entirely on someone else's actions (unless the Trigger is "whenever I want").
Delayed Effect is most often used for a power that originates in the user, and the user can choose when to set it off. Delayed Effect also requires the GM to set a value for how many Delayed Effect powers the character can have going; this is usually used in Fantasy Hero to represent spells that a character can prepare, and the number of powers the character can hold is usually something like INT/5, or EGO x 5 Active Points total, or something similar. Trigger doesn't have this latter restriction, and in fact a character with a Power with Charges and Trigger can set up all of the Charges to be triggered (e.g. land mines built as an RKA Explosion with 8 Charges and Trigger; you can set up eight land mines). Delayed Effect also takes the user a half-Phase action to set off.
They are subtly different and originated in different contexts; Trigger started out in early Champions, and was pretty much used only to represent trip wire type things, while Delayed Effect started in early Fantasy Hero and was used to represent held spells. When fourth edition came along, the rules were standardized, but Trigger and Delayed Effect weren't combined for whatever reason.
You can more or less treat Delayed Effect as a special case of Trigger, if you're the GM. In practice, a lot of things are built with Trigger that I would probably recommend Delayed Effect for instead.
Edit to add: I also allow Delayed Effect to use the "differing modifiers" rules as seen under Usable On Others. You would build the Power as it is activated, with whatever Advantages and Limitations it would take; use that Power's Real Cost as the base cost for a "creation" Power, and that Power's Advantages and Limitations would apply to preparing the effect. You might have a Power that takes an hour with a bulky spell book (OAF Bulky, -1 1/2) to "set", but once it is set all you need is a half-Phase, a sprig of holly, and a quick Gesture and Incantation, and it goes. I tend to be a little less lenient with Trigger.