Not a question of algorithm — a question of when the model is allowed to change. One retrains on a fixed snapshot; the other never really stops learning.
"Batch" here doesn't mean mini-batch gradient descent (that's an optimization detail — how many examples contribute to one weight update). It means the training regime: does the model see a full, fixed dataset before it's allowed to make a single production prediction, or does it update incrementally, example-by-example or mini-batch-by-mini-batch, as new data streams in after deployment? That distinction — fixed snapshot vs. continuous stream — determines how a model behaves when the world underneath it changes.