The Takumar is a different design -- probably a Planar design, although that's just a guess and not actual knowledge.
The Tessar is a four-element design in three groups. For several decades, the Tessar was the premium lens for many German camera makers, so don't think that it's a mediocre lens. Far from it.
Depending on your photography, the Tessar will be an excellent lens. Wide open to about f/5.6, you'll get round out-of-focus backgrounds when shooting at closer distances.
Stopped down, it's very sharp.
I've done a lot of shooting with many types of Tessars although not large format. I've never found the lens to perform inadequately.
The Tessar name is a Carl Zeiss trademark, and you'll almost always see Carl Zeiss Jena, Carl Zeiss or Carl Zeiss Jena on the face ring. Rollei made the Tessar under license for its cameras, including the Rollei 35 and 35T, the A110/E110 and others. I can't think of any others that made the Tessar under license.
The Schneider-Kreuznach Xenar is a Tessar design and performs similarly, if not identically. The (Color-)Skopar also is a Tessar design. I'm not sure the current Cosina Voigtlander Skopars are Tessar designs.
And I recall reading that Zeiss reformulated the Tessar. Zeiss never made a big deal when it reformulated its lenses.