Does Google Treat Subdomains and Subdirectories the Same?

It has pretty much been proven that while Google has made strides to treat subdomains and subdirectories as the same, that is simply not the case.

Google is the most confused organization on earth!

sub domain is totally different domain level ranking
sub directory is belong to domain level

I think what he mentioned may be a little vague. But literally, all new domains (except country level domain extensions), starts anew, meaning everything begins at 0 - that applies to domain.com and blog.domain.com.
But domain.com/blog isn't the same as blog.domain.com - the authority can be a little different at this level. domain.com/blog would have better flow of authority to the /blog, while blog.domain.com is mostly treated as a new domain instead imo, and in my experience.

ProxiesHTTP said:

all new domains (except country level domain extensions), starts anew, meaning everything begins at 0 - that applies to domain.com and blog.domain.com.

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I have ranked country subdomains like de.domainname.com for money terms, never had a problem ranking a subdomain, rather than folder; ranked rapidly on page 1 without making external links to subdomains.

But as usual SEOs do not always agree on everything. If you hear it from Mueller and do not want to believe it, then be my guest.

And btw do you know how to link properly internally? if you do not, then of course you may lose some link juice.

This seems to be a solid summary of this classic debate: https://www.searchenginejournal.com/subdomains-vs-subfolders-seo/239795/

My personal issue is the following, with madeup example:

say we have www.corporatewebsite.com
and its a company website with strong backlink following, but the ony content on the site is company story, career pages, and a very light blog. lets say this company is going to create a corporate web design service. for branding purposes, the marketing ppl want to create a brand new domain called www.dopedesign.com but the SEO guy pushes back and says we should create a landing page on the existing domain bc i has many links pointing to it and is more ready/ripe to receive leads via google traffic, whereas the brand new website will take ages to really rank well. however, now the SEO person is faced with a question - do they create www.corporatewebsite.com/dope-design or do they create www.dope-design.corporatewebsite.com ? the former has more links/equity to put to use, but it also strays from the website topical theme. whereas the subdomain is more authentic bc we want to tell google 'we understand that this design service is a bit different than the content/topical theme of our current www.corporatewebsite.com therefore we are going with subdomain.

but now my question goes back to square 1: if we are foregoing a subfolder in favor of a subdomain in order keep google happy, isn't the link power/equity that we are giving up by creating a subfolder a waste, since at that point we might as well create a new domain? TLDR: how much more equity/ranking power does a subdomain have over a brand new domain?

Generally depends how will linked the sub-domain is. If it's in the nav bar, then it will be treated virtually equally. If it's not got any links from the main site, then Google may judge it as less important.

M.C. Histemine said:

Generally depends how will linked the sub-domain is. If it's in the nav bar, then it will be treated virtually equally. If it's not got any links from the main site, then Google may judge it as less important.

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I thought that interlinking would help but I agree that the nav bar would be significantly more helpful