Trace Files : Trace file can be generated for a particular session or for all session they have extenstion .trc.These files are not readable and to read them you have to use the Tkrpof utility from the command prompt.They are found in the directory where ur user_dump_dest is pointing to in the initialization file.
Alert files : Alert files are associated with the Instance they trace all activities associated with the database for example startup and shutdown and any block corruption occuring in the tablespaces is recorded,if in case there is a database crash this is the file which you need to look at.This file also contains background process for all the Oracle Background processes.This file will be located in the where ur background_dump_dest is pointing to in the initialization file.
Trace files are text files output by the DB to report certain occurances/activities. For example, network and background processes write to trace files when there is a problem. Also, users and DBAs can request trace files be created.
One special trace file that applies to an entire instance rather than a certain process or user is the alert log.
Thus trace file = alert log is true, with the above caveats.
For generating trace files
Then only trace files are generated.
Alert files are generated by the background processes and stored in Background_dump_dest