I was recently asked this question, and I promised I'd answer it in a blog post. Your business blog is an extension of your business as well as a marketing tool. It should definitely be a part of your website. If you happen to use a separate platform for blogging than the platform your website is on, then your blog needs to match your website in its design. Exactly. As much as possible, and then your website should have a link to your blog. It should look seamless. In fact, when someone on your website clicks on your link to your blog, they should not realize [at least not a first] that they aren't on your website anymore.
Plain and simple.
The purpose of your blog is to enhance your online presence so you can further your online goals. If your blog is treated like a separate entity, then [Yes, I'm gonna say it.] you're doing it wrong.
Cousin Hunters ~ If your family website is separate from your blog, then you are missing out on potential cousin matches. Also, it makes it easier for your readers to refer to your tree or charts when they're reading your blog posts. Your blog posts are just a natural extension of your family website. No, you're not in a traditional business, but you are in the business of cousin hunting.
Genealogical Societies ~ The whole idea - the purpose - of your blog is to communicate with current members and to reach out to potential members. If you're blogging with purpose then your readers should naturally and easily be able to explore your site for more information, and you certainly do not want your blog looking separate from your website. You want it to look seamless. They shouldn't click on a link, and then wonder if their browser has been hijacked. Right? Right?
Professional Genealogists & Genealogy-Related Businesses ~ Your blog and website need to look professional. First of all, they are not separate entities. Your blog is an extension of your website. Second of all, you are branding yourself in such a way that when a person stumbles upon your site, they say, "Oh yeah. I've heard about this blog. I've gotta read it!" Wishful thinking? Maybe. Maybe not. Your blog is a marketing tool, and it's helping you to snag clients. How many times have you been on a site and you click one of their links and it looks totally different? That's not professional looking. It's distracting. The only thing a visitor to your blog should be distracted by is your writing [and in a good way]. They should be totally caught up in your blog post that by the end they want to hire you. Or by the end you've helped them out with a problem they were having in their research. And if they ever need to hire a professional genealogist or if they're ready to buy from your business, who do you think they're going to remember? The professional genealogist or company who has that awesome blog they read every week. That's who.
The Take Away
Your blog is a part of your website and if they're on different platforms, the visitor should not know it.