First of all, Amitabha is the leader of the Western Paradise. Avalokitesvara Bodhisattva assists Amitabha in guiding all sentient beings to be reborn in the Western Paradise. There is also Mahasthamaprapta Bodhisattva. The three are collectively known as the "Three Saints of the West".
There is no difference between reciting "Namo Amitabha" and "Namo Guanyin Bodhisattva". There is no difference because both Amitabha and Avalokitesvara Bodhisattva can bless all sentient beings and fulfill the wishes of all sentient beings. The difference lies in the fact that Amitabha Buddha made the forty-eight great vows to lead all living beings in the ten directions to be reborn in the Western Paradise of Paradise, where they can never turn back until they become Buddhas. Avalokitesvara Bodhisattva, in addition to assisting Amitabha in guiding sentient beings who chant Buddha's name, is mainly responsible for rescuing sufferings and providing compassionate rescue to sentient beings suffering from illness and disaster in the evil world of the five turbidities.
As for the situation in your own home, it depends on what you and your family want. Only when your wishes correspond to those of the Buddha and Bodhisattva, can your sincere thoughts be able to induce the connection between you and receive the blessings of the Buddha and Bodhisattva. If you and your family's wish is to cultivate merit and fulfill your retribution body to be reborn in the Western Paradise until you become a Buddha. This is consistent with Amitabha's great wish, so please recite "Namo Amitabha". If you and your family's wish is to maintain health, peace and happiness, then please recite "Namo Guanyin Bodhisattva".
However, we must understand one truth: If you only pursue health, peace, happiness, etc., these people will have unfulfilled consequences. When these blessings are fully enjoyed, you will still have to suffer in the six realms of reincarnation. It is very difficult to encounter the Buddha's Dharma again in reincarnation. If you don't encounter the Buddha's Dharma, you will not be able to cultivate blessings. Failure to cultivate the blessings will mean that you will fall into the three evil paths and suffer eternal eons with no escape. There is a metaphor in Buddhism that says: Just cultivating blessings is like shooting an arrow into the sky with a bow. No matter how high the arrow is shot, it will fall from the sky. This means that if you only cultivate blessings, even if you cultivate a lot of blessings, you will go to heaven to enjoy blessings. In the future, when you have enjoyed all the blessings, you will still fall down, and you will not be able to obtain the final and fundamental liberation from the sea of ??suffering. Because only by cultivating blessings and wisdom can we achieve liberation. There is a sentence in our daily recitation textbook: All Buddhas in the ten directions and three times, all Bodhisattvas and Mahasattvas, and Mahaprajnaparamita. That is to say: all the Buddhas and all the great Bodhisattvas in the ten directions and three times can only save themselves and others to the other side with great wisdom. Therefore, if you want to achieve great blessings and great wisdom, please always recite "Namo Amitabha".
Okay, Namo Amitabha!