There seems to always be confusion between these two.  First some terms:  I'm just going to say Scheduled Apex is shorthand for a class that implements the Schedulable interface.  Batch apex is shorthand for a class that implements the Batchable interface.

Scheduled apex basically allows you to schedule some type of job.  It doesn't do anything else but determine WHEN something runs, i.e., once a day, once a week, every Tuesday and Thursday of each week, etc.  Batch apex allows you to process long-running jobs, which, if run in a normal context may generate limit exceptions.  Usually Scheduled and Batch apex complement each other.  If you have a long-running batch job, you usually want to schedule that to run, say, once a week.

So at a high level, say you have a batch job (this code may not run - I just wrote it off the cuff):
<pre>
global class AccountWrecker implements Database.Batchable {
global Database.QueryLocator start(Database.BatchableContext bc) {
  return [select Id, Name from Account];
}

global void execute(Database.Batchable bc, SObject[] accounts) {
  for (Account[] batch : (Account[]) accounts) {
   for (Account acc : batch) {
    acc.Name += " just got wrecked.";
   }
   update batch;
  }
}

global void finish(Database.Batchable bc) {
  // send out an email or something to the user
}
}
</pre>

Now - you can run this one time by just doing this:
<pre>
Database.executeBatch(new AccountWrecker());
</pre>

However, say you want to have this run every hour.  You obviously don't want to wait by your computer with an alarm clock to execute the code, so you create some Scheduled apex.
<pre>
global class ZFT_GetExchangeRateScheduler implements Schedulable {
global void execute(SchedulableContext sc) {
  Database.executeBatch(new AccountWrecker());
}
}
</pre>

Now just creating the scheduled apex does not actually schedule the job.  It is just the class that Salesforce's apex scheduler knows to how to talk to to start the job.

Now you can actually schedule the job by either writing some anonymous apex using System.schedule, or by navigating in the UI to Develope > Apex Classes and clicking the "Schedule Apex" button

Hope that helps.