Can I separate website name and blog name?

I’m a new potential WP user. I want to create a website for my wife’s small business. I’d also like to help publish a blog as part of her website. Can I have a blog on the website (separate page) that has a different look and title?

I’m not sure if WP is the best tool for what I want to accomplish. I think we want a website that includes a blog, not a blog that includes a website.

Any suggestions would be welcomed. Thanks.