What does it mean by the statement: "a problem is hard to approximate "?

In most of the research papers that I have read so far, I often come across the statement of the following form: "the problem is hard to approximate within any factor smaller than some constant".

What is the meaning of hardness here? I am confused. Does it specifically mean NP-hardness or is it an informal way of saying: "general difficulty in obtaining the approximation"?

For example consider this paper. In the abstract, the authors have repeatedly written the statement of the form "hard to approximate". However, some of their inapproximability results are based on the Unique Games Conjecture. Therefore, considering "hard" to be "NP-hard" would be incorrect here. It would be great if somebody could clarify this terminology. Thank You.