Generally speaking, a Muslim has to honor all places of worship whether the place is a mosque or a musalla located in a large building or a place hired for performing prayer. In this regard, there is a difference between a mosque and a prayer hall in terms of some legal rulings that apply to both. These rulings are clarified in the fatwa below.
The Islamic Religious Council of Singapore states the following: There are two types of prayer halls: a mosque and a musalla. The Malays call a musalla “surau.” The difference between the two is that a mosque has been dedicated as waqf for salah. As a waqf, it belongs to all Muslims until the end of time. If the land is needed, the value of the property should be reinstated as waqf on other lands.
A surau however, has not been dedicated as waqf for salah. It still belongs to an individual or a company or a group of people. It does not belong to all Muslims. As such, it can be taken away without any compensation to the Muslim community.
Due to this difference, certain things that are forbidden in a mosque are allowed in a surau. For example, a menstruating woman can sit in a surau to listen to lectures or attend religious classes, but she is not allowed to do that in a mosque. The case is similar to someone who is in the state of major ritual impurity or janabah.
As for performing tahiyat al-masjid, as the name implies, it can only be performed in a mosque, not a surau.