This is second on the list of "common domainer problems with trademarks". Number one would be an undue focus on whether a mark is registered.
Trademarks come in varying degrees of strength, scope, and fame. Once you get past the initial issue of "what is a trademark", then the next thing you have to wrap your head around is "what sort of trademark are we dealing with".
"Coca-Cola" is an extremely well-known mark for a soft drink. That fame confers a scope broader than simply whether or not it is used on a soft drink. If you attempted to sell "Coca-Cola" brand clothing, the fame of the mark is such that consumers might reasonably believe the brand has branched out in to clothing.
Trademark "infringement" is when a mark is used on similar or competing goods, causing consumer confusion. There are things beyond infringement. One of those is "dilution". Trademark dilution occurs when a famous mark is subject to unauthorized use which erodes the distinctiveness of the mark.