If it's a big company, then the person that wrote the job description and the person that wrote the ad are probably completely different. I haven't seen the ad so can't comment on whether it was just a standard template ad for vacancies at the company.

If the company has a website with vacancies listed then it should be ok to use it, provided that the one you are going for is listed there, or there is some sort of commonality (ie a standard job id number) that you can use.

If the ad you saw gave the name of a specific person to send the application to, then do what they ask.

Just my $0.02.