Here is a simple, Jain-dharma based explanation.

• Gacha (गच्छा): In Digambar Jainism, a gacha refers to a traditional monastic lineage or order. It is a historical family of monks led by a particular Acharya or set of senior monks, and it preserves specific lineages, practices, and disciplinary codes within the Digambar order. Examples are the idea of organized lineages within the Digambar sangha, each with its own succession of teachers and monks.

• Sampradaya (सम्प्रदाय): A sampradaya means a broad religious tradition or school within Jainism. It denotes a distinct spiritual lineage with its own interpretations, practices, and ritual emphasis. In Digambar Jainism, sampradaya can refer to larger sectarian currents (for example, Digambar as a major sect) and to narrower sub-traditions or reformist/grouping tendencies within Digambar monks and scholars over time.

How they relate:

• A gacha is about a concrete lineage of monks within the larger sampradaya. So, you can have a Digambar sampradaya that contains multiple gachchas, each with its own line of monks and teachers.
• Differences between gachchas or sub-traditions are usually about historical succession, preferred teachers, and certain disciplinary or ritual practices, while the core Jain philosophy (karma, nyaya, ahimsa, moksha) remains the same.

If you’d like, I can look for specific Digambar gachchas and sampradayas mentioned in Jain scriptures and give you exact names and their distinguishing features.