Bodhi
Bodhi: from verbal root budhi to awaken, to understand: awakening, enlightenment, supreme knowledge. Through Bodhi one awakens from the slumber or stupor inflicted upon the mind by the defilements kilesa and comprehends The Four Noble Truths sacca Com. to M. 10.
The enlightenment of a Buddha is called sammā-sambodhi 'perfect enlightenment'. The faith saddhā of a lay follower of the Buddha is described as he believes in the enlightenment of the Perfect One saddahati Tathāgatassa bodhim: M. 53, A. III, 2.
As components of the state of enlightenment and contributory factors to its achievement, are mentioned in the texts: the 7 factors of enlightenment bojjhanga = bodhi-anga and the 37 'things pertaining to enlightenment' bodhipakkhiya-dhammā. In one of the later books of the Sutta-Pitaka, the Buddhavamsa, 10 bodhipācana-dhammā are mentioned, i.e. qualities that lead to the ripening of perfect enlightenment; these are the 10 perfections pāramī.
There is a threefold classification of enlightenment: 1. that of a Noble Disciple sāvaka-bodhi. i.e. of an Arahat, 2. of an Independently Enlightened One pacceka-bodhi, and 3. of a Perfect Enlightened One sammā-sambodhi This 3-fold division, however, is of later origin, and in this form it neither occurs in the canonical texts nor in the older Sutta commentaries. The closest approximation to it is found in a verse sutta which is probably of a comparatively later period, the Treasure Store Sutta Nidhikkanda Sutta of the Khuddakapātha, where the following 3 terms are mentioned in stanza 15: sāvaka-pāramī, pacceka-bodhi, buddha-bhūmi see Khp. Tr., pp. 247f..
The commentaries e.g. to M., Buddhavamsa, Cariyapitaka generally give a 4-fold explanation of the word bodhi: 1. the tree of enlightenment, 2. the Noble path ariya-magga, 3. Nibbāna, 4 omniscience of the Buddha: sabbaññutā-ñāna. As to 2, the commentaries quote Cula-Nidesa where bodhi is defined as the knowledge relating to the 4 paths of Stream-entry, etc.; catūsu, maggesu.
Neither in the canonical texts nor in the old commentaries is it stated that a follower of the Buddha may choose between the three kinds of enlightenment and aspire either to become a Buddha, a Pacceka-Buddha, or an Arahant-disciple. This conception of a choice between three aspirations is, however, frequently found in present-day Theravada countries, e.g. in Sri Lanka.
References
Maha Thera Nyanatiloka. Manual of Buddhist Terms and Doctrines, Buddhist Publication Society, first edition 1952.