one additional difference between chat and responses is the number model turns a single api call can make. chat completions is a single turn api primitive -- which means it can talk to the model just once. responses is capable of making multiple model turns and tool calls in a single api call.

for example, you can give the responses api access to 3 tools: a vector store with some user memories (file_search), the shopify mcp server, and code_interpreter. you can then ask it to look up some user memories, find relevant items in the shopify mcp store, and then download them into a csv file. all of this can be done in a single api call that involves multiple model turns and tool calls.

p.s. - you can also use responses statelessly by setting store=false.