you can use quotes (") to specify a phrase search in the uspto search system ...
eg. "phrase search" will look only for "phrase search" and not the "phrase" or "search" entries just by themselves ...
also you can use the logical operators of the uspto search for more precise searches ... go to uspto.gov > click e-Business ... Trademarks on the left > click search on the top > click HELP on the left (alternatively click Free Form Search from the types of searches > click HELP on the top) > then click Logical Operators from the menu ... (I could not put a link straight there because the search times out)
lastly , you can check for international trademarks , in the WIPO (World Intellectual Property Organization) with the
Madrid Express simple search or with the
Madrid Express structured search...
the basic principle behind trademarks is the avoidance of confusion (for the origin - as in from which company) of a product for consumers and the protection of a company's efforts in creating a good brand ...
if one term of the two is TMed , then it would depend on what the term is and also on what the second term is ...
eg. if the first term is "Google" (constructed term) and the second term "domains" you can understand that if you register Googledomains , people might get confused that you are selling Google domains and therefore Google would be on the winning side taking that domain from you either with a URDP (Uniform Dispute Resolution Policy) or in courts ...
on the other hand , if the one term is "apple" (generic term) and the other term is "green" you can register greenapple if you gonna use it for selling hats for example ...
the same words can be used as brands in different industries , since TMs are industry specific (eg. even though Apple is a well-known company you can use "apple" for selling hats , that is if there is not a TM for "apple" for hats) ... there are some exceptions to this , for example , if a company is really well-known (brand awareness) , also famous for a specific characteristic and another company is trying to exploit the name for association with tha characteristic ... eg. McDonalds won over a hotel company trying to name itself McSleep because the court decided that the hotel company was trying to exploit the fame of McDonalds for fast , high-in-value/price products (and that the consumers might be confused that the hotels belonged to McD) .
if a company owns a TM it can easily prevail in acquiring or cancelling TMed domains in all gTLDs and all ccTLDS of countries that it has a TMed presense in ... regarding countries they are don't have a presense at , I would suggest people should respect a brand (if they are aware of it) and not try to exploit it ... unless the term is a generic one (not a constructed word) and they have a genuine interest in developing the name in a different industry that the industries the TM holder is doing business in ...