Two people can agree they want strong coffee and want opposite drinks. One means a dark, smoky roast. The other means something that will keep them awake through a night shift. Neither is wrong, and the word is doing four jobs at once, which is why buying advice about it is so consistently useless.
Strength in coffee means one of four unrelated things: concentration, extraction, caffeine content, or roast darkness. Only the first is what the industry means technically. The other three are what people usually mean in a shop. Separating them is the whole trick.
One: concentration
This is the technical meaning. Concentration is the proportion of dissolved coffee solids in the liquid, measured as total dissolved solids and expressed as a percentage. Filter coffee typically lands somewhere around 1.2 to 1.5 percent. Espresso is far higher, often in the region of 8 to 12 percent.
Concentration is controlled almost entirely by your ratio of coffee to water. More coffee, less water, more concentrated cup. It is the only sense of the word you can change by arithmetic alone, and it is the one people most often think they are adjusting when they are actually adjusting something else.
Two: extraction
Extraction is a different axis, and confusing it with concentration causes most home-brewing frustration. Extraction is how much of the available material you pulled out of the grounds, usually expressed as a percentage of the coffee's dry mass, with a commonly cited target band of roughly 18 to 22 percent.
You can have a concentrated cup that is badly under-extracted, and it tastes sour and intense at once. You can have a dilute cup that is over-extracted, and it tastes thin and bitter. This is why "it's too strong, add water" so often fails to help: adding water reduces concentration but does nothing about a bitterness caused by over-extraction.
Three: caffeine
The most common everyday meaning, and the one with the least connection to the other three. Caffeine content is driven mostly by the species and the dose, not by how dark the roast is or how the cup tastes.
Robusta carries substantially more caffeine than arabica, roughly double by weight in most comparisons. And a large filter coffee usually contains more total caffeine than a single espresso, because there is far more coffee and far more liquid involved, even though the espresso is enormously more concentrated. The espresso tastes stronger. The filter keeps you awake longer.
Roast level barely moves it. Dark roasting burns off a small amount of caffeine, but the difference is minor and it is partly offset by the fact that darker beans are less dense, so a scoop of them weighs less.
Four: roast darkness
The supermarket meaning. "Strength 5" on a bag is a roast-darkness scale, not a measurement of anything in the cup. It tells you the beans were taken further, which produces smoke, bitterness and body, and which reduces the origin character of the coffee.
This is a legitimate preference. It is just not a strength measurement, and treating it as one is why people who like dark roasts sometimes find specialty coffee disappointingly "weak" when it is in fact more concentrated than what they had before.
What this distinction will not do for you
Knowing the four meanings will not make you like a coffee you do not like. Preference is real and it is not a knowledge deficit. Someone who genuinely enjoys a dark, smoky, bitter cup is not making an error that education will correct.
It will also not help you order in a café, because the vocabulary is not shared. Asking for something "strong" will still get you whatever the person behind the counter assumes you mean. The useful move there is to describe the outcome, not the word: more caffeine, or more concentrated, or darker roasted.
The honest recommendation
Work out which of the four you actually want, then change only the matching variable.
Want more caffeine? Drink more coffee, or choose a blend containing robusta. Want a more concentrated cup? Change the ratio, and start by going from 60g per litre to about 70. Want less bitterness? That is extraction, and the levers are grind size and brew time, not dose. Want the smoky flavour? Buy a darker roast and stop calling it strength, because that word will send you to the wrong shelf.
None of this requires buying anything, which is why it is worth saying plainly. The single most useful purchase in this whole area remains a scale, and we do not sell those either.