My understanding as a non-lawyer is that a TM is territorial - with respect to geography and product area. For example, a computer company might register the TM "Fire" in the US. That does not mean that you cant reg. fire.com, but would be wise to avoid sticking content and especially adsense about computers.
Some TMs are felt to be so widely recognised that a dilution effect might be felt to occur. These are huge names like coke and disney. Regging these are more likely to be a TM issue, and are less defensible (if at all) under the UDRP process.