yes there is a difference. Statement of undertaking is a letter with an assurance that you will fulfill an obligation that you agreed on, which is stated in the letter.
it is much like a conforme, you will conform with what is stated on what you signed.
so once you signed / acknowledge this you agree to it.
Now lets look at it this way, making and issuing a policy is management prerogative. You as a supervisor, no matter if you agree to it or not, are bound to implement it. if you signed it, there will be no problem. but if you don't sign it, it will send a wrong signal to management that you oppose to them. Better think about this cause this will affect your career in that company.
Now, another way to look at it. The policy they are releasing is not something new.
You as a supervisor is a part of managerial employee. It is inherent to a supervisor, to be responsible to people in those care. You are there to supervise their work and implement management decision. Your staff are your responsibility and what ever happens you are also part to blame if anything goes wrong because they are your responsibility.