I have recently been looking into incorporating the machine learning release for iOS developers with my app. Since this is my first time ever using anything ML related I was very lost when I started reading the different model descriptions that Apple has made available. They have the same purpose/description, the only difference being the actual file size. What is the difference between these models and how would you know which one is best fit ?
The models Apple makes available are just for simple demo purposes. Most of the time, these models are not sufficient for use in your own app.
The models on Apple's download page are trained for a very specific purpose: image classification on the ImageNet dataset. This means they can take an image and tell you what the "main" object is in the image, but only if it's one of the 1,000 categories from the ImageNet dataset.
Usually, this is not what you want to do in your own apps. If your app wants to do image classification, typically you want to train a model on your own categories (like food or cars or whatever). In that case you can take something like Inception-v3 (the original, not the Core ML version) and re-train it on your own data. That gives you a new model, which you then need to convert to Core ML again.
If your app wants to do something other than image classification, you can use these pretrained models as "feature extractors" in a larger neural network structure. But again this involves training your own model (usually from scratch) and then converting the result to Core ML.
So only in a very specific use case -- image classification using the 1,000 ImageNet categories -- are these Apple-provided models useful to your app.
If you do want to use any of these models, the difference between them is speed vs. accuracy. The smaller models are fastest but also least accurate. (In my opinion, VGG16 shouldn't be used on mobile. It's just too big and it's no more accurate than Inception or even MobileNet.)