Accepted Practice for Appointment Orders
Accepted practice from several decades and still applicable to the majority of companies is that, for jobs offered on contract, fixed-time hire, and on rolls, there should be a hard copy of the appointment order—one given to the employee and another for HR. However, you can provide a letterhead copy to the employee, and for the HR copy, you can take a photocopy after their signature.
Use of Email for Freelancing Work
You are correct that only an email may be given for some freelancing work, especially in a continuous assignment arrangement between the freelancer and the company. However, it is suggested, advised, and better not to follow this practice for other types of job allocations.