• Dept of VA
As noted in the previous responses by my colleagues, this is a highly variable question depending on both your geographic region and operating sector. If in the US, the difference between a contract with a private entity or a government entity frequently dictates whether "calendar day" or "business day" applies. In your specific case, neither the Contractor nor the Consultant controls; guidance must be obtained from the dual questions, "What is written in the contract?" and "Under what jurisdiction is the contract written?"
Herr Neumann has already mentioned the significance and high value placed on specific word choice in German contracting. This kind of specificity requires an understanding of regional contract terms, as all countries in the EU have both shared contract law and individualities which apply based on historic practice, national individualities, etc. If you are operating in a country or region where sharia law applies (the Iranian oil bourse in Kish springs instantly to mind), the default definition of "days" may be very different than that applied in common law European contracting, the various North American court-centric contracting practices, or Asiatic contract practice.
Although you mentioned it is "not specified", if you are working in the US, there are peculiarities applicable to contract law which divide between public and private enterprise. One example is the "Christian Doctrine". It only applies to government contracts, but it boils down to "if the government forgot a clause which it normally uses, it's still constructively in the contract, and that's the risk one takes dealing with the government." Obviously, private industry would not condone that kind of practice, but this applies in the public sector.
Regardless of region, in your situation, it is usually the case that the tendency is to construe the meaning of "days" as whatever is most lenient to the party (or parties) who did not write the contract. So if your company wrote the contract, the language will be most strictly enforced against you. If the Contractor wrote it, you have a better argument that your intent was working days, and there was no "meeting of the minds" on the issue.
Either way, your situation appears to require both legal assistance (check with your legal department) and some mediation/negotiation. The contractor wants calendar days, so they are apparently comfortable following a more stringent timeline than the one desired by the consultant. Take into consideration the parties' reasons for arguing that their definition applies. The Contractor wants to get the job done quickly (is there a performance incentive involved for early/timely completion?), while the consultant may have their evaluative credibility at stake and therefore want more time to ensure complete reviews of the contractor's work.
Without further information, any further answer given here is guesswork or too vague to be of use, and probably won't help you much. Take this as a process improvement opportunity to ensure all your contract personnel are trained to include definitions of the word "day" in all documents from this point forward. In most places, the nature of contract language means writing "days" in a contract without further definition makes only one group of people happy: Contract dispute law firms, who bill by the hour world-wide.