Liturgy

Liturgy, with which litany is sometimes confused, is a word principally used in the context of religion, and, for most native English speakers, the Christian religion. OED (1903) says "A form of public worship, esp. in the Christian Church", and specifically the service called the Holy Eucharist. Within the liturgy, there can be a litany: "A form of public prayer, consisting of a series of requests to God in which the clergy lead and the people respond" (after OED, 1903).

So litany is closer to list than liturgy is. If you mean the words of a prayer, say litany; if you mean the words of an entire Church service, say liturgy; and if you are not concerned with religion, avoid these two words and try list instead.

The word liturgy is older than Christianity. Its first appearance is in the classical Greek form λειτουργία (leitourgia), meaning 'public service, service of the gods, public worship' (OED). Litany comes from a Greek word (λιτανεία, litaneia), meaning 'prayer, entreaty'.