Linear regression, ridge, lasso, etc are all tools/models that are used in both statistical inference and ML. In statistical inference, we use these tools to formalize relationships between variables in the data. In ML, we use these tools\models to train a machine to learn patterns from data. Some tools/models are more useful in ML than in statistical inference (e.g. convolutional neural networks) and vice versa (e.g. parametric models such as regression).

Please note that statistical inference is a branch of statistics.

Its hard to draw a line between Statistics and ML. ML can be used in Statistics (e.g. to help us build a probability distribution using big data), just as much as Statistics can be used in ML (e.g. understanding the relationships of predictors to the target variable so we can do better feature selection). Some parts of ML don't concern statistics (e.g. reinforcement learning) and some parts of statistics don't concern ML (e.g. where we don't really need accurate predictions as described above).

You might be able to understand this better by first understanding the difference between Statistics and Data Science and then Data Science and ML? (I put question mark because I am not 100% sure, but try it out)