The type of hair addition that can be styled in various ways and is not sewn into the hair is referred to as:

The correct answer is clip-in extension because this type of hair addition is designed for easy application and removal, allowing for versatility in styling. Clip-in extensions are typically made with small clips attached to wefts of hair, enabling the user to quickly and securely add length or volume to their existing hairstyle without the commitment of more permanent methods like sewing or bonding.

This flexibility is key, as it allows individuals to change their look on a daily basis, with the ability to easily take them out when not needed. If you consider the other options, wigs are full headpieces that generally cover the hair completely, making them less versatile for styling in diverse ways as they are not meant to blend seamlessly with the natural hair. Wefts refer to strips of hair that can be sewn in but do not offer the same removable convenience. Braiding is a technique used to style hair itself rather than applying an addition, which means it doesn't directly relate to the concept of hair extensions.