Summary: Bhuta Yajna means offering of cooked foods to all living beings as part of the Pancha Yajnas to be done by a householder. Bali refers to the Cooked food that is offered.
The five great yajnas ordained for a Grihastha are collectively known as Baliharanam or Balivaiśvadeva. These five Yajnas have been explained as follows:
यदधीते स ब्रह्मयज्ञो यज्जुहोति स देवयज्ञो यत्पितृभ्यस्स्वधा करोति स पितृयज्ञो यद्भूतेभ्यो बलिं हरति स भूतयज्ञो यद्ब्राह्मणेभ्योऽन्नं ददाति स मनुष्ययज्ञ इति॥६॥
What one studies is Brahma Yajna, what one puts in the fire is the Deva yajna, what one gives to the forefathers while saying Svadha is the Pitr Yajna, what Bali one offers to the beings is called Bhuta yajna and what food one gives to Brahmins is called Manushya Yajna.
-Baudhayana Grihya Sutra Praśna 2, Adhyaya 9
To understand what the terms Bali and Bhuta, in the above sutra mean:-
The procedure for the above Baliharanam is found in Chapter 8 of Praśna 2 of the Baudhayana Grihya Sutra and the mantras to be used for the entire procedure is derived from the Ekagni Kanda of the Taittirya shakha of the Krishna Yajurveda. The chapter starts with the words by explaining what Baliharanam means:
अथ बलिहरणम्। सायं प्रातर्यदशनीयस्य क्रियेतौपासने पचवे वा होम:।
Now the Baliharanam. (Explained as) In the evening or morning the cooking or oblation (homa) of the food in the Aupasana fire.
Ahead in the procedure, it describes how the food is given to the devatas while saying svaha, to the forefathers while saying svadha and for the Bhutas by throwing in the sky.
This clears the meaning of Baliharanam which means offering (haranam) of the cooked food (Bali) to devatas, Pitrs and bhutas.
As stated, in the Baliharanam, one of the offering (bali) is made to the bhutas. One can see from the dictionary, one of the meanings of bhuta is a being or creature. This is the meaning applicable to the case. Let’s see how.
The abovementioned chapter 8 of the Baudhayana Grihya sutra describes the procedure for the Bhuta Yajna portion of the Baliharanam. The grihastha must throw the food towards the sky and chant the mantra (Baudhayana 2.8.38/39), taken from the 1st Prapathaka, 1st khanda of the Ekagnikanda of the Krishna Yajurveda, shows us that the Bhuta refers to living beings or creatures. The relevant mantra is as follows:
ये भू॒ताः प्र॒चर॑न्ति दिवा॒ नक्तं॒ बलि॑मि॒च्छन्तो॑ वि॒तुद॑स्य॒ प्रेष्याः॑ । तेभ्यो॑ ब॒लिं पु॑ष्टि॒कामो॑ हरामि॒ मयि॒ पुष्टिं॒ पुष्टि॑पतिर्दधातु॒ स्वाहा॑॥
The commentary describes the emboldened line as - those beings who roam around in the day and night, offering Bali to those. (यानि भूतानि इतस्ततश्चरन्ति - जो प्राणी यहाँ से वहाँ विचरण करते हैं।)
The same has also been explained in the Manusmriti 3.90:
विश्वेभ्यश्चैव देवेभ्यो बलिमाकाश उत्क्षिपेत् ।
दिवाचरेभ्यो भूतेभ्यो नक्तञ्चारिभ्य एव च ॥ ९० ॥
The offering to the Viśvedevas he should throw into the sky; as also to the beings roaming in the day and to those roaming at night.—(90)
He should gently place on the ground food for dogs, outcasts, Cāṇḍālas, persons afflicted with filthy diseases, birds and insects.—(92)
If you talk of the word ‘Elementals’ like fire etc., then as per the procedure described in the Sutra, only Agni (2.8.9), water (2.8.33) and Prithvi (2.8.33) are included, but in the devatas and not even mentioned together. Thus ‘Elementals’ like water fire etc is an incorrect meaning for Bhuta Yajna.
Thus it is amply clear that Bhuta means beings or creatures, whether diurnal or nocturnal.
Bhuta Yajna means offering (Haranam) of cooked food (Bali) to the other creatures (Bhuta) roaming around.
You can read about an article of Balivaiśvadeva by Gayatri Parivar, which briefly explains Bhuta Yajna and how Hindus are supposed to care for all living beings.