Ballonné and Ballotté are similar, both in name and structure, but there are marked differences. How do we designate the differences and pass those ideas on to our students?

To make it short and simple:  BalloNNé is a BouNce and BalloTTé is a Throw.  Ballonné bouncing on one foot and ballotté throwing energy from one foot to the other, front to back.  N's and T's are a quick memory device to help you (and your students) keep these terms straight, but let's dig a little deeper and explore the origins and the imagery that can bring the vocabulary to life in your classroom.

First, it's important to know that neither ballonné (sometimes spelled balloné) or ballotté were included in the 1787 Dictionnaire de Danse.  Why?  They were rather late additions in the grand scheme of physical ballet vocabulary, as most of the earlier work was focused on terre à terre (floor to floor) movement and not on the strong jumps and leaps that we idealize today.

Ballonné came to be before ballotté:  ballonné showing up in the 1895 Dictionnaire de la Danse and ballotté coming into more common usage in the 20th century.  If you think about the structure of the movement, this evolution makes sense.  Ballonné connecting to the beginning of pointe work and advancing to a jumping movement.  Ballotté being a more advanced jumping movement, which would have been more highly valued in the the 20th century.

Ballonné - Pronounced [balɔne] "bal" pronounced like beginning of the word "balance," "o" pronounced like the o in "on," "nné" pronounced like "nay" but trying to avoid pronouncing the final Y as we do in English.

Ballonné has the quality of bouncing like a ball.  It comes from the word ballon in French, which is simply an air-filled ball.  The bouncing movement is repeated on a single supporting leg and the working leg progresses from a cou-de-pied in plié to an extended leg at the height of the jump.
Much like a bouncing ball, this movement can stay in place or travel by advancing the supporting foot.  (Note:  You'll find the word ballonné elsewhere in French but with a different meaning.  Outside of dance, ballonné means air-filled or swollen like a balloon.)

Ballotté - Pronounced [balɔte] "bal" pronounced like beginning of the word "balance," "o" pronounced like the o in "on," "tté" pronounced like "tay" but again trying to avoid pronouncing the final Y.

Ballotté has the quality of being tossed from side to side (or more commonly front to back in this case).  "Pas de danse qui combine un sauté dessous avec un développement effacé."*  [Dance step that combines a jump underneath one's self with a lengthening/dévloppé in effacé]. The word ballotté is most often used to describe a boat or piece of debris that is tossed by the harsh waves of the sea.  You can visualize both the tossing action and the shape of the boat in the step itself.  The dancer jumps bring the feet underneath him/herself at the height of the jump landing on one foot and extending the other through a développé to the front (or back) as the dancer comes into plié on the supporting foot.  The step is generally repeated with a second jump where the feet are pulled underneath and the opposite leg is extended through développé to the back.   Imagine a boat being thrown by the waves during a storm.  Or picture the boat itself:  the extension of the leg in front creates the front of the boat with the toes being the tip of the boat and the extension of the leg in the back creating the back of the boat.  As the movement is repeat and the energy is tossed from front to back, you can almost see the body of the boat in the dancers legs in feet.

*Trésor de la langue française - http://atilf.atilf.fr