It's probably coincidental that they share the same first 4 letters. The sound is different with 'coch' having a hard 'ch' sound.
You may have seen the feminine variant of 'coch' in the course which is 'goch'. This means exactly the same as 'coch'
In Welsh adjectives often have different forms to match masculine or feminine nouns (like French petit and petite for example)
For variants of red there are words like 'fflamgoch' (flame red) and also the use of other adjectives as in English 'coch tywyll' = 'dark red'.