How to check with PHP if the script is being run from the console or browser request?

Use php_sapi_name()

Returns a lowercase string that
describes the type of interface (the
Server API, SAPI) that PHP is using.
For example, in CLI PHP this string
will be “cli” whereas with Apache it
may have several different values
depending on the exact SAPI used.

For example:

$isCLI = (php_sapi_name() == 'cli');

You can also use the constant PHP_SAPI