Quite simply, a laboratory-grown diamond is a diamond: carbon atoms arranged in a diamond cubic crystal structure. The only difference between mined diamonds and lab grown diamonds is the origin of the diamond. Grown diamonds and mined diamonds have the exact same physical properties.
A cubic zirconia is not a diamond. It is merely a diamond simulant, meaning that it looks similar but not exactly like a diamond. In fact, a cubic zirconia contains zero carbon, whereas diamonds (mined and grown) are made entirely from carbon.
Put another way, cubic zirconia is a cheap imposter to a diamond that is a different material entirely; whereas a synthetic diamond from Ada Diamonds is chemically and optically indistinguishable from a mined diamond.