A Canadian citizen applying at a port of entry pays the fees CBP collects at the time, while an employer filing Form I-129 pays the USCIS filing fee and any premium-processing fee. Current amounts are listed in the USCIS fee schedule, Form G-1055, and should be checked before filing.
Budget by route, then add the cost of getting the evidence right
The two routes carry different fee structures. In-person application at the border involves the CBP fees collected at the port, and the money is small compared with the cost of a refused entry after a long drive. A petition filed by the employer involves the USCIS Form I-129 fee, the asylum program fee where it applies, and premium processing if the employer wants a fast answer; the fee schedule changes periodically, so the G-1055 is the only figure worth quoting.
Beyond government fees, budget for a credential evaluation if the transcript is unusual, for an adviser's time to review the employer letter, and for translations if any document is not in English. Ask the employer in writing which fees it will pay, because some cover petition costs but not the applicant's travel or dependants' expenses. A TD family member's application carries its own fee.
Hypothetical example: Hector, a Canadian zoologist, receives two offers: one asks him to seek TN classification during travel and the other will petition first. He should compare written estimates that separate government charges, credential work, travel, dependant costs and optional expedited processing. The offer letter is the record that settles who has promised to pay which expense.
Do not treat a refundable airline ticket or hotel booking as proof that the application is ready; the professional eligibility file, not the travel spend, decides the admission question.