You are better to put your blog and website together instead of having it on two domains if your blog contents are relevant to the niche of website. If it is a general blog or a blog with different niche you're better go with seperate ones.
Here are some advantages if blog and website are not on seperate domains.
1. Ease of use - People may find it easier to navigate or bookmark your contents
2. Credibility - If your blog and website are on the same domain then users will come to know that the blog belongs to the same website only.
3. Better SEO - If all the relevant contents of the blog are related to the website niche on the same domain it will bring more organic search traffic.
4. Updation - As blogs are frequently updated than a website pages your overall domain feels and looks like refreshed. Thus more incoming traffic.
5. Social media integration - There is a better way to integrate with all social media pages of the website and blog. So more centralised link building and user shares in common.
So make your blog and website together on a single domain if both are of a same niche or a closely related subject.