I work in an accountancy practice and would be happy to shed some light on this for you.
The date of appointment is the date that appears on Companies House.
Directors contribute to National Insurance differently than employees. Directors get ALL of the NI allowance up front and will not pay contributions until their NIable earnings for the year reach the Primary Threshold (PT). This is £8,164 for 17/18, £8,424 for 18/19.
The appointment date is used to apportion this threshold for the year, therefore if the appointment date is 6th April the director will receive the full allowance for the year. However, if the director is appointed in July the threshold will be apportioned for 9 months of the tax year.
Once their earnings reach the PT they will pay 12% (assuming they are on NI rate A) on all their earnings until they reach the upper earnings limit (UEL). This is £45,000 for 17/18, £46,350 for 18/19.
A director is taxed in the same way as an employee.
I hope this makes sense. If you do have any questions please do not hesitate to private message me or reply on this thread.