Actually, they both do the same thing, but attack different sides of the mood slope.
Which you'd know, if you ever stopped to consider how to adjust your mood with either.
Caffeine introduces anxiety and irritability on downslope, after about two half-lives, or 12-ish hours (6 hour half life). On the up slope, caffeine provides a long slowly declining period of alertness and performance. The initial buzz comes on strong and tapers off over time.
People seek caffeine to perform. But a slow sinking feeling appears near the end of the day.
Nicotine modifies mood on the other side of the bend, with it's presence evening out irritability with immediate relief. The trail off goes unnoticed until a sudden urge kicks in, to bump one's self back up onto the plateau.
Nicotine is sought to cure or cool an immediate pang, which leaves the impression of easing into relaxation, which degrades silently until suddenly noticed as an urge to re-up.
The perception of nicotine is downtime, even though the dosage process and serum curve is the usual spike and tapered downslope, people learn modify the nicotine downslope differently, by catching the drop-off before cravings become desperate.
Which is why cigarettes are designed as they are, and achieve product success the way they do. Metering doses at an almost hourly rate, with twenty dose packs marketed to afford exactly that behavior.
Coffee, as a liquid, is readily either sipped or chugged as needed, and has different preparation and consumption habits, so its marketing is different.
Caffeine's downslope is handled differently, since the withdrawal effects, are separated by longer distances of up to 48 hours, and because circadian rhythms are more drastically effected. Consuming in the late afternoon results in insomnia, so the better choice is to cure the anxious late day mood disruptions with food and alcohol, and stave off withdrawal (vasodilation migraines, etc) the next morning.