The short confession is Ashamnu. The long one is Al Chet. Both are alphabetical, listing sins according to the Hebrew alef-bet.
The use of the alphabet is not just a sign of poetic cleverness; it was an aid to memory in days when printing had not been invented and few people had prayer books. An acrostic device was used by many of the authors of the poetical passages that intersperse the High Holyday prayers.
The sages say that better than both the confessions is the simple statement, “Truly we have sinned”.
One of the great differences between Rosh HaShanah and Yom Kippur is that it is only on Yom Kippur that the confessions are said, not on Rosh HaShanah.
The reason may be that on Rosh HaShanah we rise above the theme of wrongdoing to a level of perfection where sin does not exist.
Rosh HaShanah is the dream – one world, peaceful, productive, filled with blessing and joy. Yom Kippur is the mundane reality – the dream that often goes wrong when we seek to implement it.
Yet we need both – Rosh HaShanah to remind us what to hope for, Yom Kippur to recognise how hard it is and to urge us to turn mis-steps into mitzvot.