Probability theory, optimization, statistics and so forth do not differ between economics and computer science, so it makes sense they are the same.
You would see a difference in that these sort of models are used for causal inference and counterfactual analysis, whereas Machine Learning is mostly predictive.
That being said, Machine Learning is starting to apply methods developed in econometrics and/or stats, like GMM and Time Series methods.
For example, Long-Term Memory models are quite recent additions to Machine Learning. The short-memory process restriction of autoregressive models has been worked on since the early 80's.
You would see a difference in that these sort of models are used for causal inference and counterfactual analysis, whereas Machine Learning is mostly predictive.
That being said, Machine Learning is starting to apply methods developed in econometrics and/or stats, like GMM and Time Series methods. For example, Long-Term Memory models are quite recent additions to Machine Learning. The short-memory process restriction of autoregressive models has been worked on since the early 80's.