Are the Eagle Talon and Mitsubishi Eclipse just the same car under different names? What differences, if any, are there between the two?

They are basically the same car along with the Plymouth Laser. Chrysler and Mitsubishi had an engineering and marketing relationship for about 20 years starting in the 1970s.The only differences between the cars were minor: different grills, different taillights.

https://lexusenthusiast.com/forums/threads/mm-retro-write-up-mitsubishi-eclipse-plymouth-laser-eagle-talon.6149/

The Eagle Talon and Mitsubishi Eclipse are basically siblings, built on the same platform with shared engines and drivetrains thanks to a Chrysler-Mitsubishi partnership in the '90s. What sets them apart is their personality:
The Talon feels more aggressive and stripped down inside, aimed at raw performance. The Eclipse is smoother in design, a bit more refined inside, and marketed as more upscale. They're like two versions of the same song, one played loud and fast, the other with polished harmonies.

https://differencebetweenshoes.com/eagle-talon-vs-mitsubishi-eclipse-a-90s-sports-car-showdown/