Contracted beasts were different from Innate Beast.
Innate Beasts already have their own set of skills that they can use depending on their grade. They could understand their summoner clearly and hence would be able to execute their commands more fluently. This was also the reason why most of the time, the summoners would always prioritize on nurturing their Innate Beast rather than focusing on the contracted beasts that would die and was not even eternally loyal.
Contracted Beast on the other hand would need to sense their summoner's orders before they could execute their skills. If the beast has low intelligence, and was not familiar with its summoner, there was even a chance that it would not follow the command of its summoner and not execute its own skill.