Puja is the common term for ritual worship, of which there are numerous synonyms such as Archana, Vandana, Bhajana, etc., though some of these stress certain aspects of it.
The object of worship is the Ishta Devata or guiding Deity or the particular form of the Deity whom the devotee worships—Narayana or Vishnu as such, or His forms as Rama and Krishna in the case of Vaishnavas, Siva in His eight forms in the case of Saivas and Devi in the case of Saktas.
The devotee selects sometimes his Kuladeva or Kuladevi, family Deva or Devi, for his worship. Sometimes, the Devata is chosen for him by his Guru or spiritual preceptor.
Sometimes, he himself chooses that Devata which most appeals to him. This form is his Ishta Devata.
An object is used in the outer Puja such as an image (Pratima), a picture, or an emblem such as Saligrama in the case of Vishnu worship or Linga in the case of worship of Siva.
Whilst all things may be the objects of worship, choice is naturally made of those objects which, by reason of their effect on the mind, are more fitted for it.
An image or one of the useful emblems, is likely to raise in the mind of the worshipper the thought of a Devata. Saligrama stone induces easily concentration of mind.
Everybody has got predilection for a symbol, emblem or image. Idol or Murti (Vigraha), sun, fire, water, Ganga, Saligrama and Linga are all symbols or Pratikas of God which help the aspirants to attain one-pointedness of mind and purity of heart.
These are all personal inclinations in the worshipper due to his belief in their special efficacy for him.
Psychologically, all this means that a particular mind finds that it works best in the direction desired by means of particular instruments or emblems or images.
The vast bulk of humanity are either of impure or of weak mind. Therefore, the object of worship must be pure for these people. The objects that are capable of exciting lust and dislike must be avoided. But, a higher, advanced Sadhaka who has a pure mind and who sees the divine presence everywhere and in everything, can worship any kind of object.
In Puja, an image or picture representing some divine form is used as the object of worship. The image is adored. All image, a Sila or Vigraha or Murti, represents the particular Lord who is invoked in it.
A Linga represents Siva. It represents the secondless, formless Brahman. The Sruti says: “Ekamevadvitiyam Brahma—The Brahman is one alone, without a second.” There is no duality here. A Linga is shining and attractive to the eyes. It helps concentration. Ravana propitiated Siva and obtained boons by worshipping the Linga.
A Saligrama is an idol of Vishnu. Saligrama is the symbol of Vishnu. There are images of Sri Rama, Sri Krishna, Karttikeya, Ganesa, Hanuman, Dattatreya, Sita, Lakshmi, Parvati, Durga, Kali, Sarasvati, etc., according to the taste of the particular devotee.
The images of Vishnu and of His Avataras, and the images of Sakti and Siva, are the popular idols that are worshipped both in temples and in the houses.
The idols in the temples of Tirupati, Pandarpur, Palani, Katirgama, etc., are powerful Deities. They are Pratyaksha Devatas. They grant boons to the devotees, cure their ailments and give Darsana. Wonderful Lilas are associated with these Deities.
There is no polytheism in Hinduism. Siva, Vishnu, Brahma and Sakti are different aspects of one Lord.
God reveals Himself to His devotees in a variety of ways. He assumes the very form which the devotee has chosen for his worship. If you worship Him as Lord Hari with four hands, He will come to you as Hari. If you adore Him as Siva, He will give you Darsana as Siva. If you worship Him as Mother Durga or Kali, He will come to you as Durga or Kali. If you worship Him as Lord Rama, Lord Krishna or Lord Dattatreya, He will come to you as Rama, Krishna or Dattatreya. If you worship Him as Christ or Allah, He will come to you as Christ or Allah.
You may worship Lord Siva or Lord Hari, Lord Ganesa or Lord Subrahmanya or Lord Dattatreya, or anyone of the Avataras, Lord Rama or Lord Krishna, Sarasvati or Lakshmi, Gayatri or Kali, Durga or Chandi.
All are aspects of one Isvara or Lord. Under whatever name and form, it is Isvara who is adored. Worship goes to the Indweller, the Lord in the form. It is ignorance to think that one form is superior to another.
All forms are one and the same. Siva, Vishnu, Gayatri, Rama, Krishna, Devi and Brahman are one. All are adoring the same Isvara.
The differences are only differences of names due to differences in the worshippers, but not in the object of adoration. It is only out of ignorance that different religionists and different sects fight and quarrel amongst themselves.