No, it is not the same. Distantly supervised systems are a particular type of semi-supervised systems.
In a way, one can describe the difference as follows.
A semi-supervised system has in input a dataset in which some examples are labeled correctly and some are not labelled at all.
A distantly supervised system has in input a dataset in which all examples are labeled, but some are labelled incorrectly. Usually such a labeling is done by a baseline algorithm, so you also can think of such a system as having two inputs: (1) an unlabeled dataset and (2) a low-quality heuristics to label it. (In addition, a distantly supervised system can also have access to another dataset that is labelled correctly and/or to another dataset that is not labeled at all.)
Since a distantly supervised system can be thought of as using an unlabeled dataset, it is usually considered a particular type of a semi-supervised system.
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