They are difficult to compare because they are intended to solve different problems. Typical learning algorithms have access to the entire, pre-labeled training set, which they can repeatedly iterate over.
Online learners are still trained using a completely-labeled data set, but they cannot access the entire data set at once. Instead, examples arrive one at a time and cannot be saved or replayed.
In active learning, the labeled data can be processed in batches, but the learner either has access to additional unlabeled data or can generate new examples itself. During training, it can request that some of these examples be labeled. Imagine asking a teacher for help.
Online learning makes sense when you have so much data that you cannot possibly store it all; active learning makes sense when you have less labeled data and the labeling step is expensive.
Online learners are still trained using a completely-labeled data set, but they cannot access the entire data set at once. Instead, examples arrive one at a time and cannot be saved or replayed.
In active learning, the labeled data can be processed in batches, but the learner either has access to additional unlabeled data or can generate new examples itself. During training, it can request that some of these examples be labeled. Imagine asking a teacher for help.
Online learning makes sense when you have so much data that you cannot possibly store it all; active learning makes sense when you have less labeled data and the labeling step is expensive.