Suggestions on how to explain 'models' & 'algorithms' I guess other members of this Stack have ran in to this before, but I may be wrong: Have you ever been approached and asked to explain the difference between models and algorithms? This happened to be recently and, while I feel that I explained it well, there is a colleague whom disagrees with my assessment..

How I see the two:

Algorithms: Used to train a model, that is, give it instructions and process the input.

Model: A diagram of sorts, that incorporates utilizing algorithms to train inputs. Can be reused on similar data.

Pre-Trained Model: A model, usually trained on larger data sets and can be utilized to build [your] own models with other data.

Thoughts? I'd appreciate them to see if I am just completely off base here.
I think your definitions are mostly right....I would add that model is a specific implementation of algorithms designed to handle a specific issue or group of issues
Regarding pre-trained model, my understanding is that it can be used to build other models indeed, but the main use case is simply using it to predict or classify on new data, having already been trained previously