Stem tendrils and leaf tendrils both …

Stem tendril provide support to the plant while leaf tendril helping in the formation of food by the process of photosynthesis. Stem tendril is made up of hard and strong fibres to provide rigidity for plant while leaf tendril is made up of soft fibres.

A tendril in botany is a specialized stem, leaves or petiole that is threadlike in shape and is utilized by climbing plants for support, attachment and cellular invasion by parasitic plants. Tendrils don't have lamina or blade but are able to carry out photosynthesis. 

In a stem tendril the terminal bud is modified to be tendrils where the growth occurs with the help of axillary bud. This helps the plant body to climb e.g Grape vine and Passion fruit

On the other hand, 

In a leaf tendril the entire leaf is modified into a tendril this helps in climbing plants or twining around suitable host. The leaf tendril helps a vining plant to secure itself through possessing a twining growth habit