Speaking as someone who cut out caffeine cold turkey, it's a different thing

I got stinking headaches for a week, but not an overwhelming urge to drink caffeine

When smokers quit, they almost always describe the urge to smoke rather than the physical side effects, often described more like hunger.

I've done this several times, I have a headache for 24-48 hours then pretty much back to normal. Tolerance takes longer to reset obviously and I'm sure I get more energetic in subtle ways I'm unaware of in there... but I don't think it's remotely comparable to a serious addiction, from what I've read tobacco is probably the most widely accepted thing able to cause that level of addiction.

There's got to be more to this because even though I consume prolific amounts of caffeine I do not experience any pain on cessation. Yet, many of my coworkers do feel this pain.