What is the difference between using the Stability AI API versus just running Stable Diffusion locally?

I am building a side project that involves generating images programmatically and I am trying to figure out the right infrastructure approach. I could run Stable Diffusion on my own hardware or a cloud GPU instance, or I could use the Stability AI API directly. I want to understand what the practical differences are between those two approaches before I decide which direction to go.

My project needs to generate a relatively high volume of images, probably several hundred per day at scale, and the cost per image matters a lot at that volume. I also care about the range of models available and whether I can use the latest Stable Diffusion versions without having to manage my own model downloads and updates. The maintenance overhead of running my own instance is something I am keen to minimise given I am doing this as a side project alongside a full-time job.

Has anyone built something using the Stability AI API and found the cost and reliability acceptable for a production use case? I want to understand the pricing model clearly, whether there are rate limits that would constrain a higher volume workflow, and whether the API gives you access to the same model quality as running the latest SD versions locally or whether there is a quality difference between them.