Powershell has two different kinds of errors that have slightly different semantics.
Terminating errors are produced using the throw keyword in powershell, or by any exception thrown by regular .NET code. These can generally be handled the same way as exceptions and caught with try/catch statements, or using the powershell trap (details of which are not worth going into here).
Non-terminating errors are generally created using the Write-Error cmdlet. These will get written to the output stream as ErrorRecord objects and usually printed in red text just like terminating errors, but the script will continue. However, if $ErrorActionPreference is set to Stop, all non-terminating errors will be treated as terminating errors. This includes being caught by catch blocks and trap statements.