One wonders what the difference is between Ganesha Jayanti and Ganesha Chaturthi, or Sankashta Hara Chaturthi which comes once every month. It is, of course, a mythological event of a "birth" with a mythological date.
Ten days of Ganesh Chaturthi are thus set aside every year to remember Him reverently, glorify Him, and worship Him. According to our ancient Indian philosophy Shri Ganesha is the first "shabda" (AUM) or vibrations manifested when the manifest Universe begins.
Hence He is associated with the "beginning." Some people have loosely described him as the "Lord of Beginning." The word "shabda" is usually wrongly translated as the "word" or "sound." These "vibrations," that are ubiquitous in the Universe, are not mythological entities but verifiable perhaps with modern scientific techniques.
However, the attribution of a quality of supreme knowledge and primordial design of the multidimensional universe in invisible form entailed in this entity of "vibrations" is still difficult for the human mind, trained in modern science to comprehend.
Western science, is not equipped to comprehend this "greatest shabda" which is the beginning of the Universe with all of its order, beauty, magnificence, creativity, as well as the chaos, disorder, destruction and dissolution, all programmed into this incomprehensible "shabdabrahma" which was identified with the sound "OM."
This sound in turn may have the closest resonance with the original shabda, which does not require the presence of air to vibrate and exist, as it predates the origin of air. The ancient Tantric philosophers were ingenious in using symbols that had the power to reach the deepest layers of the human mind and they were also expert iconographers with enormous creativity that would capture the fancy of multitude of generations that had a sincere desire to be curious about the nature of the Universe.
They also understood the meditative techniques that could be successfully used to gain insight into the "para-vidya" and hence they transformed "OM" first into a symbol and then anthropomorphized it into an image for personal and group worship (and of course, meditation). They built this image into a mythological human form with a head that had resemblance to the elephant head.
This created the mystique of the form of Shri Ganesha which baffled many Indian and Western scholars who had no access to the original Tantric esoteric or arcane knowledge. The reason to place quotation marks around the word Hindus is that the word "Hindu" did not exist when the concept of "OM" and "Shri Ganesha and Ganapati" emerged in ancient India.
Many uninformed Hindus have learned about their culture and their religion from these erroneous English or European translations that are essentially demeaning or ignorant representations of their Hindu culture, religion, and their Hindu objects of worship which are naturally merely viewed as "curiosities" by the Westerners who did not have any respect for the profound philosophy or the insights into the cosmogony that the ancient Indian Vedic culture had elaborated over the ages. 'Om-kara' personified is Shri Ganesha.
It is also known as 'Pranava' or a precursor of 'Praan Shakti', at the beginning of the creation. To understand the true nature of the Universal Consciousness, the Human Consciousness has to go beyond or cut through the "Prakriti" by meditating on the primordial Universal Shabdabrahman "OM."
This process is known in Yoga as "pratiprasava." It literally means retracing steps of the process of emergence of human consciousness. Opposite of "jagat" or "jaga" is "gaja" a word that stands for the "elephant."
The Tantric mystics had a message beyond the simple coincidence that the symbol "OM" turned 90 degrees clockwise assumed the likeness (or the shape) of the elephant's head. Meditating on "OM" can lead to the identification with the Universal or Cosmic Consciousness. Such identification can occur only in the Fourth state of Consciousness or "Turiya."
This state of consciousness is experienced as the most enjoyable bliss (and therefore, "Modaka"- that which gives bliss and joy- is the name given to the sweet pastry which is offered and is in the hand of Shri Ganesha.) The secret message of the Tantrik Ganesha image and its birth on the fourth day of the Lunar calendar every month is that the Vedic culture values the emergence of this "fourth" state of consciousness in which as if the Ganesha is potentially born in any human mind.
The Hindus and the followers of the Vedic culture revere Ganesha as the Ultimate Absolute or the Shabdabrahma and worship Him on the Chaturthi of every Shukla paksha or the fourth day of the waxing moon every month.