The first difference is that Weka's OneR can only predict nominal class values, while DecisionStump is able to predict both nominal and numeric values.

The algorithm used by OneR is:

For each attribute,
    For each value of the attribute, make a rule as follows:
        count how often each class appears
        find the most frequent class
        make the rule assign that class to this attribute-value
    Calculate the error rate of this attribute’s rules
Choose the attribute with the smallest error rate

(Source: Data Mining with Weka — Lesson 3.1 Simplicity First! by Ian H. Witten, page 5. See https://www.saedsayad.com/oner.htm for a worked example.)

In contrast, for classification problems, DecisionStump determines the split by using entropy. For regression problems, DecisionStump chooses the split that minimizes mean square error.