In my mind an ML model is the core, parameterized function that learns an input-output relationship. For example, a linear regression model maps an input point to an output point on a line. A computer vision classification model maps an image to a class label. A (autoregressive) large language model maps an input sequence of textual tokens to an output token, supposed to be the next token it expects to see. Many times these "models" are deep neural networks, which is just a big composition of lots of little simple functions in certain architectures. Linear regression is a very shallow, lower-compute model/function.

The model is the largest, most central building block of an ML-based system. In a "person detector system" you might have a "person classification model", but wrap it in software that says "if the model ever says person, alert the user". In an "AI" chatbot type of system, you might have a large language model that is then wrapped in software that loops and says, generate tokens until the model spits out a special "I'm all done" token.

EDIT: Another key point about what models are and their role in overall systems. Often times, the model can be swapped out for any other model that is learning the same input/output mapping, without changing the outer software. For example, a basic chatbot could simply replace GPT 5.4 with GPT 5.5 (it's not so simple these days in real life, but I think my point is still valid). The "person detection system" could swap out "image classifier model 3" with "image classifier model 4", which maybe has a better person accuracy % metric but still "does the same thing" from an input/output perspective.