It would be more usual in English to refer to steps rather than stairs or staircase.We might consider this issue a bit further. In Malay, there is just one term: tangga. In contrast, in English there are two terms: stairs if they are inside a building; and steps if they are outside. We can say that Malay only has the superordinate (more general term), while English only has the hyponyms (more specific terms).
Of course, it can work the other way round, as with padi/beras/nasi in Malay compared to rice in English (something I have discussed before here).
Superordinate/hyponym differences such as this can easily give rise to problems in translation.
Actually, there are some other differences in the two versions on the sign. A literal translation of the Malay would be: "It is forbidden to run when climbing up or down the steps of the tower". I'm not sure why the English version is so much shorter, though certainly the contrast is not quite as large as in other signs I have seen (e.g. here).
