Traditional casual inference was focused on cases where any confounding was caused by a known set of linear confounders. In this case, straightforward application of linear regression or other GLMs can be used to produce causal estimates. If you have a huge number of potential confounders or if you are worried about non linear terms or interactions between confounders, then those traditional approaches do not work.
Causal ML approaches have worked out the theory to allow you to use flexible machine learning estimators to remove the impact of these other variables so that you can get an unbiased estimate of the causal effect of your treatment variable.
Traditional casual inference was focused on cases where any confounding was caused by a known set of linear confounders. In this case, straightforward application of linear regression or other GLMs can be used to produce causal estimates. If you have a huge number of potential confounders or if you are worried about non linear terms or interactions between confounders, then those traditional approaches do not work.
Causal ML approaches have worked out the theory to allow you to use flexible machine learning estimators to remove the impact of these other variables so that you can get an unbiased estimate of the causal effect of your treatment variable.