If you use your incorporation's business number, then the corporation is the employer, not you. The payroll number is not different except for the two letter designation at the end. RP stands for payroll, RC stands for corporation, RT stands for GST/HST etc.
You may use the corporation for contract work done by yourself, but your corporation is still the employer. If this is just for a caregiver, I would call the CRA and make a new business number, in your name, as a sole proprietor just for the caregiver. It just makes it easier for book keeping, because the business number is just for that use, and no other.
As well you may have a RP account in your corporation, that is for business use, not for a caregiver. The RP account done for the caregiver is for the caregiver ONLY, no other use
Some people mistakenly will use their corporations RP account, for a caregiver, this is incorrect, and can cause you A LOT of headaches moving forward if not done correctly
There are RP accounts for regular employees, however the Government puts caregivers into their own category, hence they get their own RP account