No, Google AdX is not the same as Google Ad Manager. (Linking of accounts to be mentioned) Google Ad Manager is an ad server that enables publishers to set up, serve ads, and track revenue. Whereas, Google AdX is a programmatic exchange where publishers can find buyers and advertisers.
Google Ad Manager gives access to Google AdX (conditions applied) as well as other marketplaces like Adsense, (open bidding) PubMatic, Magnite, Index Exchange, AppNexus.
Google Ad Manager comprises AdSense, (link- Google Analytics as well as Ad Exchange). Google AdX gives the publisher complete control, and higher demand, and lets you define the price floor.