The function system_get_date_types($type = NULL) is deprecated; instead use system_get_date_formats($date_format_name = NULL).

These two functions both return an array of date formats, but the keys for the return values are different. This change was made during the conversion into configuration files instead of storing in the database. See the code from system_get_date_formats() for more information on the difference in return values.

Drupal 7:

// Gets the list of defined date formats and attributes.
$date_types = system_get_date_types();
foreach ($date_types as $machine_name => $value) {
  $date_formats[$machine_name] = check_plain(t('@name format', array('@name' => $value['title'])) . ': ' . format_date(REQUEST_TIME, $machine_name));
}

Backdrop:

// Gets the list of defined date formats and attributes.
$date_types = system_get_date_formats();
foreach ($date_types as $machine_name => $value) {
  $date_formats[$machine_name] = check_plain(t('@name format', array('@name' => $value['label'])) . ': ' . format_date(REQUEST_TIME, $machine_name));
}
Introduced in branch: 
1.0.x
Introduced in version: 
1.0.0
Impacts: 
Module developers
Related Github Issues: 
https://github.com/backdrop/backdrop-issues/issues/530