That looks like a glass mug. And a mug can very easily be interchangeable with the term 'cup' in normal speech.
Regarding the image posted, it might commonly be referred to as a 'mug', 'cup', or even a 'glass' (assuming it's made of glass).
2023年1月20日
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Technically it is a mug. Cup doesn’t Reallt have that handle. But there are times I have called that a cup also.
2023年1月20日
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It is a mug. A cup would usually have a matching saucer. In recipes you will see 'add one cup of water', that is a measurement equal to 250ml.