Dark roasted coffee is widely assumed to be stronger. The roast determines flavour and solubility rather than potency, and the two are frequently confused because one tastes like the other.
Roasting changes the bean before brewing begins
Green coffee has almost none of the aroma associated with the drink, and roasting generates it through browning reactions between its sugars and proteins.
As roasting continues, those origin-derived acids and sugars are progressively consumed and replaced by compounds created by the roasting itself.
A light roast therefore tastes more of where the coffee grew, and a dark roast tastes more of the roasting process, which is a difference in character rather than in concentration.
Caffeine survives roasting largely intact
Caffeine is stable at roasting temperatures and does not break down appreciably, so a bean loses very little of it however dark it is taken.
Roasting does drive off moisture and burn away mass, so a darker bean is lighter and a scoop measured by volume contains more beans.
Measured by weight the difference in caffeine between roast levels is small, and the effect of dose and brewing method is far larger than the roast.
Dark roasts taste strong because acidity has gone
The acids that give a light roast its brightness are largely destroyed by longer roasting, leaving bitterness and roast flavour unopposed.
Bitterness reads as intensity, so the cup is perceived as strong even where less coffee has actually been extracted.
Lighter roasts retaining their acidity taste lively rather than powerful, which is why they are often mistaken for weak coffee.
Roast level changes how the bean brews
Darker beans are more porous and brittle, so they grind more finely at the same setting and give up their solubles faster.
That makes them prone to over-extraction, which adds harshness, and is why dark roasts are often brewed coarser or for less time.
Light roasts are dense and release solubles slowly, requiring hotter water, finer grinding or longer contact to extract fully.
Strength is set by the brew, not the roast
The concentration of a cup depends on the ratio of coffee to water and on how thoroughly that coffee is extracted.
Any roast can produce a concentrated or a dilute cup, since those are decisions made at the point of brewing rather than at the roastery.
Choosing a roast is therefore a flavour decision, and choosing a strength is a separate one made with the scale and the kettle.