Full disclosure I have no opinion on whether or not models are moral patients. I haven't kept up with it.
Simplifying a lot: Diffusion models are a way to learn "diffusion dynamics", which is to say a process that turns a signal (a specific distribution of data) into noise (e.g. random normally distributed points) and vice-versa. What this means is that you're learning to remove noise iteratively so that eventually a random collection of points resembles a specific distribution or joint distribution.
How you represent these dynamics, what the points and their trajectories represent, depends on domain. In images, the points are images in terms of "features", which are like parts of images. In theory they could be pixels but this wouldn't work very well well at all. In principle, you can think of a bunch of dimensions of images, stuff like noses, faces, landscapes, etc and diffusion as a data-dependent (i.e. "learned") process for figuring out how to blend these together. Going from words to features is a separate process and I'm not going to cover it, the short version is that there's another learned process for doing this.
Prompting diffusion models tends to suck. A lot of the open source models are, and I'm not kidding at all here, trained by weaboo hentai enthusiasts on anime image databases where everything is done with tags, so to prompt them directly you need to do so in terms of tags. This has improved some over time but usually by gluing a huge language model to them.
There are a few further caveats wrt your question about how different this is from a language model:
Language models are typically downstream of transformer models. Historically diffusion models were not. You represented diffusion dynamics as a different kind of neural network (a "convolutional" network). It turns out transformers work pretty well for vision as well, so nowadays a lot of diffusion models are also a kind of transformer.
What we think of today as LLMs aren't just doing language modeling. They're also doing preference and value modeling, which were not present in the original next-token predictor models. Diffusion models don't really do anything similar to this for the most part.
The image generators you use through ChatGPT or other large AI services are doing a fair bit of preference/value modeling, because they tend to be image generator models that a language model can interact with.
Not all image generators are diffusion models, some are based on other techniques like visual autoregressive scaling.
Make of that what you will, I guess.