Is an underground mine collapse or a tunnel collapse called a sinkhole?
This is probably more of an English language question than a science question. 
The answer to it depends on the extent of a person's vocabulary &amp; knowledge of a particular field of engineering.

Over a period of time, in the media I have read &amp; heard mine "tunnels" incorrectly being called shafts. Mine shafts are vertical or near vertical. What most people call mine "tunnels", people in the industry call drifts or drives - these are horizontal or near horizontal. The word tunnel is better applied to civil items of infrastructure rather than mines: such as rail or vehicular tunnels or tunnels to access underground bunkers or storage facilities.

Similarly, a tunnel or mine collapse could be termed a sinkhole and people not familiar with either the civil engineering or mining fields might do that - particularly journalists. People in the civil or mining fields would use terms such as tunnel collapse or mine subsidence hole.