Ninjutsu one of three basic all ninja most learn to grow. There are different types of Ninjutsu that are based of natural and transformation depending on the use of the chakra and jutsu. Medical, cursed ninjutsu, space-time, reanimated etc. It was adopted by ninja from the ridoku to teach originally the love and connection of ninja through chakra. But through the ages the teachings of ninshú it was branch down to control the chakra and energy around one through nature to manipulate objects or elements.
Summoning is using specific space-time ninjutsu to transport a animal or creature from far away or other realm through a certain amount of blood need for sumomoning.
Some summoning have respect and loyalties to certain ninja or villages that have learn to summoning certain allies for battle and support in battle reasons.
Summoning contract is a scroll that the ninja uses to put their own blood, in order to make a agree through your blood and Chakra and instructor. This contract is between you and the creature that is based on the type of animal or fighting support needed through molded Chakra synching the blood and contract signer.
Snake summoning is the direct contract seal with the snakes and of other snakes that come from ryúchi cave were the snake sage lives. Depending on the Chakra used and strength of the ninjutsu. This contract is special because of the bond and usage the snake have and different support and task they can manage will in battle and for sensory purposes.
Summoning rites Imy not to sure but from what I believe it is the different limiters and movement to the snakes when summoned and the time frames there able to move dependent or on command. But like I said not to sure needs your help with that explanation before you hit ,enter with the training.