@sfkiwi Hey Michael, I’m a fellow noob in this vast world of machine/deep learning.
Now, some parts of what you said were absolutely correct. Machine learning involves a lot more identifying features of interest and fiddling around with them to suit your model (this is called feature engineering) and deep learning uses a generic equation and backprop to find the optimal weights. However, for the other stuff, I think you have it the other way around. Deep learning is a subset of Machine Learning. There are tons of other techniques which have been around for years including KNN, K-means, SVM, Random Forest and so on. Neural Networks (Deep or Shallow) are just one method that can be used from a plethora of options. Each algorithm suits a particular task better and sometimes we use a collection of these techniques together (see boosting and bagging).
Having said that, deep learning is the technique that is revolutionizing the industry and academia. It’s giving us the results that were unprecedented.
For a good overview of machine learning and it’s algorithms, I suggest you look at the ML course from fast.ai itself or the popular machine learning course on Coursera.