Need a 48v relay but I don't know the terminology
The relay will control a 48v 32a circuit. 


Your relay will require a coil voltage to suit your control circuit voltage. You haven't stated this as other than "signal".

The contact(s) will require a rating of &ge; 48 V DC and &ge; 32 A DC. (note capital 'V' for volt and 'A' for ampere.) 


  It should be normally open unless a signal is present. 


Almost all relays feature a normally open (NO) contact. One with a changeover contact can be used. The normally closed (NC) contact would be left unterminated.


  The relay will not be on a PCB or rack of any kind, but probably mounted on a plywood board.


You are looking for a panel-mount relay base.


  Does such a relay exist? How would it be described? 


Yes. Described as 48V DC plug-in relay with 32A DC NO contact.


  Someone said I'd need to amplify the small signal in order to control large contactors. Is that true, and if so, how would I configure (or describe) that?


Please edit your question to supply details of the "small signal".


  If someone has a specific brand or part to recommend, that would certainly be welcome.


Part recommendations and where to buy them are off-topic on this site.