what are the different between those two
Hello and thanks for asking!
In my experience these are largely the same thing - it’s a liquidated damage if a breach of contract (such as delivering late) is specified in the contract and a consequential damage if not. Does that make sense? I can elaborate further if needed (boarding a plane in a few)
A consequential damage is a damage that results from some other cause. For example: earlier this spring, on my project site, there was a vent installed in a roof that was not installed properly and as a result the insulation and gypsum below the opening were ruined when rains came. It was a consequence of the faulty installation that the other materials were damaged.
Liquidated damages are arguably a specific type of consequential damages, (Schiff Harden Lecture [4?] is a good resource). For example: A project that foregrounds energy efficiency and user’s well being is delayed at no fault of the owner or architect the owner has to pay for higher energy bills while using their dank soulless dimly lit musty haunted building for longer than planned and has been unable to complete edible landscape elements within their optimal timing.