Open source = you download the model, run it where you want, modify if needed. But you manage the infra. Examples: Mistral, Llama, DeepSeek.
Proprietary = you use a vendor's API, everything is managed. But you pay per use, your data passes through their servers. Examples: GPT, Claude, Gemini.
TL;DR: open source for control/GDPR/cost at scale, proprietary for max performance/simplicity/time-to-market.