It is important for a business website to use the same domain to send and receive email. Apart from the fact that it looks far more professional, it also helps with overall reputation of your domain.
When your website is sending email to customers (such as e-commerce communications, newsletters and even responses to enquiries from Contact Forms) it is best to have those communications coming from the same domain name as the website.
Using an personal email address or an address attached to one of the large ISP’s (such as firstname.lastname@example.org) is asking for trouble when it comes to email deliverability.
I have written in this blog about email deliverability.