There are different kinds of birth in Buddhism, depending on what realm one is reborn in.
What are these kinds of birth?
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To an enlightened Buddha, everything is merely elements (dhatu), sense phenomena (ayatana) & aggregates (khandha). 'Birth' ('jati') means to impute the idea or worldly convention of 'selves', 'persons' or 'beings' ('satta') onto the mere elements, sense spheres & aggregates (refer to SN 12.2; SN 5.10; & SN 23.2). All 'births' ('jati') are mere thought conceptions or sankhara (refer to SN 22.81). Ajahn Buddhadasa said:
The word "birth" refers to the arising of the mistaken idea "I," "myself". It does not refer to physical birth, as generally supposed. The mistaken assumption that this word "birth" refers to physical birth is a major obstacle to comprehending the Buddha's teaching. Whenever there arises the mistaken idea "I," the "I" has been born; its parents are ignorance and craving. The kind of birth that constitutes a problem for us is mental birth. Anyone who fails to grasp this point will never succeed in understanding anything of the Buddha teaching.
In the Theravada Abhidhamma, four different kinds of birth are recognized1, namely:
egg-born beings (Aṇḍaja), such as birds, fish and reptiles.
womb-born beings (Jalābuja), such as mammals. Egg-born beings are also included in this category.
moisture-born beings (Saṃsedaja), includes certain lowly forms of animals, such as worms.
spontaneously-born beings (Opapatika), such as petas and devas. These beings are generally invisible to the physical eye.
1 Comprehensive Manual of Abhidhamma, Ch. 5: "Compendium of Matter", p. 256, by Ven. Bhikkhu Bodhi