Fixed adjective - Having been established and usually not subject to change.
Regular is a synonym for fixed in conforming topic. In some cases you can use "Regular" instead an adjective "Fixed", when it comes to topics like periodic.
Regular adjective - Appearing or occurring repeatedly from time to time.
Fixed is a synonym for regular in property topic. Sometimes you can use "Fixed" instead an adjective "Regular", if it concerns topics such as uniform, even, established, orderly.
Both words in one sentence
- Casualty: has a regular turnover of cast and no fixed stars so everyone gets a storyline.
Source: Ensemble Cast
- This was partially fixed in a patch, but he still shows off his double-jointed knees◊ on a regular basis.
Source: Off Model / Video Games
- It was fixed, though, in subsequent patches, turning it from a Game Breaker to a regular gun, and then to a Joke Gun.
Source: Video Game / Modern Warfare
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Google Ngram Viewer shows how "fixed" and "regular" have occurred on timeline