There are some synonyms for puja (पूजा) like vandana (वंदना), archana (अर्चना) and stuti (स्तुति).
Is there any difference among them?
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This is a good question.
Let me first state the authentic 9 processes of the topmost yoga system (Bhakti Yoga) under which these processes are recommended:
Prahlāda Mahārāja said:
2)chanting about the transcendental holy name, form, qualities, paraphernalia and pastimes of Lord Viṣṇu,
4)serving the lotus feet of the Lord,
5)offering the Lord respectful worship with sixteen types of paraphernalia,
6) offering prayers to the Lord,
7) becoming His servant,
8) considering the Lord one’s best friend, and
9) surrendering everything unto Him (in other words, serving Him with the body, mind and words)
—these nine processes are accepted as pure devotional service. One who has dedicated his life to the service of Kṛṣṇa through these nine methods should be understood to be the most learned person, for he has acquired complete knowledge. (SB 7.5.23-24)
Of the 9 processes, hearing and chanting are considered to be the seed of rest 7.
Number 5 is archna(अर्चना) or worshiping the Deities of Lord Vishnu, which is described in proper detail and followed in some temples completely. The articles generally used are incense stick, lamp, flowers, water, a handkerchief, etc.
Number 6 is vandanam, which is offering prayers to Lord.
The term puja(पूजा) is a broad term. It's equivalent translation is "worship". This can be one of 9 forms above, but generally as per social norms, in Hindu civilization, this directs to archanam (number 5).
In technical terms, as already explained it can be one of above 9. Worship is not the external process of offering archana to Deities, it means, worshiping or glorifying The Supreme Personality Vishnu or His representatives or expansions from the heart in a favorably devotional mood.
Example - Vyasa Puja (Worshiping the spiritual master (guru) as representative of Vyasadeva, the literary incarnation of Krishna Himself as per SB 1.1.7). Govardhan-Puja, etc. not only invloves archanam but various other items such as their glorification.
stuti(स्तुति), or Vedic Hymns, as I research is same as vandanam or a particular category of vandanam that 'praise' Krishna (Eg. Kunti stuti, Brahma stuti, etc.) which are nothing but prayers offered by them to glorify Krishna.
Since Sanskrit is very technical, grammatical and rich language, one word is used in various contexts, which are deep wisdom individually. One such reference where stuti is categorized as praise to Lord is (SB 11.11.34-41)