Yes, you’re reading it correct as per Google webmaster central blog Google has re-branded it with Google Search Console. The idea behind re-branding is there are users using webmaster tools as a hobby, small business owners, freelancers, experts in their own field, marketers using webmaster tools on the regular basis to improve their business websites. The Google search console includes everyone who cares about their work and wants their work to be appearing online.
Since the webmaster tools helping the website owners from last 10 years or so, but it reflects as “Webmaster” the webmaster term defines someone who is managing websites coding, errors, development, content upload and managing content management systems. The traditional idea limited to some of its users with webmaster tools expertise. After re-branding, the company