From memory, a tower needs to be 150m to be considered a "skyscraper" these days. It's 300m and above for a "super-tall building".
The "official" definition is:
A Skyscraper: A high rise building that is used for habitable purposes may considered to be called a Skyscraper if any THREE of the following conditions are met, a Super Tall Building requires ALL conditions to be met:1. Its height is more than 40 London double decker bus high.
2. Its roof touches the clouds.
3. The water in an Olympic sized swimming can emptied from the top floor and doesn't reach the ground before the pool has run dry
4. 1% of the people of Wales (or 0.25% people of Belgium) when standing on each others shoulders couldn't clean all the windows safely.
5. An average person's neck will become strained if looking at the top of the building from 7 football pitch lengths away.
6. 100 giraffes, or 50 African elephants standing on top of each other couldn't graze off the roof garden, when standing at street level.
7. It is used in local media file footage to indicate how important the local city has become.
8. The construction firm has to re-finance at least once during the building phase.
9. A cheese sandwich when dropped off the roof will destroy anything it hits on the ground
10. The planning enquiry takes longer than does the construction.