Regardless of whether it is a breakthrough case or just simple vaccination side-effects, any symptom should demand further investigation, if it becomes concerning enough to put you off of regular tasks, or there is a possible risk of contagion.
Both breakthrough cases and post-vaccination symptoms, in the case of COVID-19, can have some symptoms, such as:
-Fever (low or moderate grade temperature)
-Fatigue and weakness
Not only are these symptoms very common with both breakthrough cases and vaccination side-effects, there can be some less common symptoms, such as skin rashes, gastrointestinal symptoms, which could also be expected.