Generally [not particualrly] Theravadin speak of an all-knowingness that has little to do with the omniscient mind as presented by Mahayana teahcings.

A short 'definition' of omniscience, given by Geshe Gyaltsen:

The 'ultimate consciousness' that is the direct realization of emptiness and the 32 qualities - the ten powers, four fearlessness and eighteen unshared qualities - are parts of the omniscience, that is, they are omniscience. The 32 qualities are 32 branches of omniscience.

Omniscience is the 'wisdom truth body', one the two bodies of the dharmakaya. While the 'naturally abiding linage' (suchness with defilements) is that which is suitable to become the 'nature truth body', the 'developmental linage' is that which is suitable to become the 'wisdom truth body', the omniscient mind of a buddha.

Before actualizing fully qualified special insight, calm abiding and special insights are two different mind. At the fourth preparation on the access level, there is a union of calm abiding and special insight, whereby they become one and the same mind. In a similar fashion, the omniscient mind of a buddha is a non-conceptual great compassion, a non-conceptual bodhicitta, the exalted wisdom, etc. as one and the same mind.

1. Texts on Buddha nature, such as Maitreya’s Sublime Continuum: The Essence of a One Gone Thus, with Commentary by Gyaltsap Darma Rinchen, and so forth.
2. Tsongkhapa's Middle-Length Lam Rim or Great Lam Rim, chapter on Special Insight.
3. Maitreya's Ornament of Clear Realization: A Commentary on the Prajnaparamita.

Generally [not particualrly] Theravadin speak of an all-knowingness that has little to do with the omniscient mind as presented by Mahayana teahcings.

A short 'definition' of omniscience, given by Geshe Gyaltsen:

The 'ultimate consciousness' that is the direct realization of emptiness and the 32 qualities - the ten powers, four fearlessness and eighteen unshared qualities - are parts of the omniscience, that is, they are omniscience. The 32 qualities are 32 branches of omniscience.

• the omniscient mind of a buddha is free from all defilements - free from the two obscurations - and thus its suchness is called 'suchness without defilements' (nature truth body)
• the omniscient mind of a buddha is the only one mind that realizes the two truths (or 'the mode and varieties') directly simultaneously. Whenever cnventionalities appear to a sentient being, they appear together with the appearance of true existence because sentient beings have not abandoned knowledge obscurations (even a bodhisattva on the tenth bhumi). A buddha is the only being free from this [type of] dualistic appearance
• the omniscient mind of a buddha is free from conceptualization (and thus unmistaken)
• the omniscient mind of a buddha knows all existent of the three times
• the omniscient mind of a buddha realizes its object newly, that is by its own power
• the omniscience knows all the different aspects of each of the disciples.

Omniscience is the 'wisdom truth body', one the two bodies of the dharmakaya. While the 'naturally abiding linage' (suchness with defilements) is that which is suitable to become the 'nature truth body', the 'developmental linage' is that which is suitable to become the 'wisdom truth body', the omniscient mind of a buddha.

Before actualizing fully qualified special insight, calm abiding and special insights are two different mind. At the fourth preparation on the access level, there is a union of calm abiding and special insight, whereby they become one and the same mind. In a similar fashion, the omniscient mind of a buddha is a non-conceptual great compassion, a non-conceptual bodhicitta, the exalted wisdom, etc. as one and the same mind.

1. Texts on Buddha nature, such as Maitreya’s Sublime Continuum: The Essence of a One Gone Thus, with Commentary by Gyaltsap Darma Rinchen, and so forth.
2. Tsongkhapa's Middle-Length Lam Rim or Great Lam Rim, chapter on Special Insight.
3. Maitreya's Ornament of Clear Realization: A Commentary on the Prajnaparamita.