Federated learning typically aims to train a central model on separate datasets without aggregating them to one location. The two main variants of federated learning are named dependent on the consistency of the data across the datasets.
Horizontal federated learning, also known as homogeneous federated learning, builds the central model on distributed data where the data at each site has the same schema. That is, the set of features are consistent across sites. For example, you could have multiple banks each with data that contains exactly the following information for each entry: account balance, age of account, credit score. This consistency allows for simpler training where local models can be trained directly on local data and the updates can be directly incorporated into the central model.
Vertical federated learning, also known as heterogeneous federated learning, builds the central model on distributed data where the data at each site has different feature sets. Extending the above example, suppose now you have credit card companies that have additional financial information in the form of timing and amount of spending. This presents challenges to federated learning algorithms by introducing the need to map entities across datasets in a privacy-preserving way.