Depends on the usage. "Corporate" refers specifically to a corporation,while "Company" is a more generic term that can also refer to other types of business entities.

"Corporate" is an adjective. There are two nouns, "Corporation" and "Company." In ordinary speech they are almost interchangeable. However, there are technical legal distinctions between the two. A "company," literally, just means a business with more than one person in it. John Doe is a shoemaker. He hires several people to work for him. Now he is "John Doe and Company" or "The John Doe Company." I think "corporation" might be similar to "S. A." in France. A "corporation" is a special legal entity. A corporation has to file papers with the state. A corporation has to make reports. There are special laws that apply to corporations. One of the most important is that the officers of the corporation do not have personal liability if the corporation goes bankrupt. Let's say the company goes bankrupt. The president of the company has $10,000,000. The company owes a supplier $2,000,000. The company only has $1,000,000. The supplier takes the company to court. The supplier gets $1,000,000 from the company. Now the supplier says "You owe me $1,000,000 more, I am going to sue the president, too." The lawyer says "You can't win. The president is not liable for the company's debts."