Both are Jain Śvetāmbara groups, so their basic Jain beliefs are the same:

• 24 Tirthankar
• Soul (jīva), karma, rebirth, moksha
• Ahimsā, aparigraha, anekāntavād, 5 mahāvrat etc.

The differences are mainly in practice, discipline and outer form, not in core Jain philosophy.

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1. Gyan Gacch (ज्ञान गच्छ)

This is a Śvetāmbara Mūrti‑pūjak gacch (lineage).

Typical points:

• Mūrti‑pūjā

- Worship of Tirthankar idols in temples (derāsar) with dravya‑pūjā: jal, chandan, pushpa, dīp, naivedya, etc.

• Āgams & tradition

- Accept Śvetāmbara Āgams and traditional commentaries. - Strong emphasis on śruta‑jñān (scriptural study) – that’s why name “Gyan” (knowledge).

• Sādhus / sādhvīs

- Stay near or connected with temples. - Typical mūrti‑pūjak dress and muhapattī (generally tied).

• Lay practice

- Temple-centred life: abhiṣek, pūjā, āratī, mangal‑dīvo, pratimā‑yatra, pilgrimage, etc.

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2. Shraman Sangh (Shraman Saṅgh / Jain Shraman Saṅgh)

Generally this refers to the Śvetāmbara Sthānakvāsī Jain Shraman Sangh.

Typical points:

• Non‑mūrti‑pūjak (Sthānakvāsī)

- No idol worship, no dravya‑pūjā, no temple‑idols. - Focus on bhāva‑pūjā: internal devotion, meditation, pratikraman, sāmāyik, svādhyāy.

• Āgams & tradition

- Also accept Śvetāmbara Āgams, but stress: - simplicity, - non‑ritualistic approach, - more inner austerity than outer show.

• Sādhus / sādhvīs

- Live in sthānak / upāśray (simple halls), not idol‑temples. - White clothes and muhapattī held rather than usually tied; stricter in some conduct rules (e.g., on movement, possessions, contact).

• Lay practice

- Satsang in sthānak / upāśray, gīt, pravachan, meditation camps, pratikraman. - Generally avoid flower‑use, idol‑decoration, and elaborate rituals.

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In short

• Common: Jain fundamentals (Tirthankar, karma, moksha, ahimsā, anekānt, etc.).
• Main difference in belief‑expression:

- Gyan Gacch: Accepts and promotes idol‑worship with rituals as valid form of Jain devotion. - Shraman Sangh: Teaches that idol‑worship and such external rituals are not necessary, and gives priority to inner spiritual practice without idols.

So the “difference in belief” is how to worship and practice, not about the basic Jain siddhānt itself.