Difference between min_samples_split and min_samples_leaf in sklearn DecisionTreeClassifier

From the documentation:

The main difference between the two is that min_samples_leaf guarantees a minimum number of samples in a leaf, while min_samples_split can create arbitrary small leaves, though min_samples_split is more common in the literature.

To get a grasp of this piece of documentation I think you should make the distinction between a leaf (also called external node) and an internal node. An internal node will have further splits (also called children), while a leaf is by definition a node without any children (without any further splits).

min_samples_split specifies the minimum number of samples required to split an internal node, while min_samples_leaf specifies the minimum number of samples required to be at a leaf node.

For instance, if min_samples_split = 5, and there are 7 samples at an internal node, then the split is allowed. But let's say the split results in two leaves, one with 1 sample, and another with 6 samples. If min_samples_leaf = 2, then the split won't be allowed (even if the internal node has 7 samples) because one of the leaves resulted will have less then the minimum number of samples required to be at a leaf node.

As the documentation referenced above mentions, min_samples_leaf guarantees a minimum number of samples in every leaf, no matter the value of min_samples_split.

Both parameters will produce similar results, the difference is the point of view.

The min_samples_split parameter will evaluate the number of samples in the node, and if the number is less than the minimum the split will be avoided and the node will be a leaf.

The min_samples_leaf parameter checks before the node is generated, that is, if the possible split results in a child with fewer samples, the split will be avoided (since the minimum number of samples for the child to be a leaf has not been reached) and the node will be replaced by a leaf.

In all cases, when we have samples with more than one Class in a leaf, the Final Class will be the most likely to happen, according to the samples that reached it in training.

In decision trees, there are many rules one can set up to configure how the tree should end up. Roughly, there are more 'design' oriented rules like max_depth. Max_depth is more like when you build a house, the architect asks you how many floors you want on the house.

Some other rules are 'defensive' rules. We often call them stopping rules. min_samples_leaf and min_samples_split belong to this type. All explanations already provided are very well said. My cent: rules interact when the tree is being built. For example, min_samples_leaf=100, you may very well end up with tree where all the terminal nodes are way larger than 100 because others rule kick in to have stopped the tree from expanding.