Thanks for you reply.
I might have explained myself poorly but the client mentioned the word 'retainer' as a kind of contract where they pay me a fixed income in exchange for my 100% availability for any work they want me to do. They would pay for the work on top of that income as well. If I accept I get a more stable income but I might miss on interesting work opportunities. Is this what you refer to as retainer? Or is there a different word for this concept? It's almost like a call option in financial markets.
I think your definition is the more standard one. I think the parent post meant to say "deposit". Retainer is usually "$2000/month for up to 20 hours of work".