Rasa = is both a noun and a verb
Rasa = feelings (n)
Rasa = feels (v)
Sedih (sad) is a good benchmark to test the dif. between merasa & berasa.
A. Mimi berasa sedih.
B. *Mimi merasa sedih.
We only say A in Malay.
This makes berasa an actual bout of sadness felt by Mimi.
Because sadness is never a constant feeling, we know that berasa (sedih) marks actual (sad) experience.
By inference merasa would be marking a constant feeling as sedih isn’t our normal mental state.
In contrast we may have both for gembira (happy)
C. Saya merasa gembira.
D. Saya berasa gembira.
Our common sense tells us that happiness may be a base feeling as well as an actual episode of happiness felt by somebody due to an event or food or occurrence.
We then establish that
Saya berasa gembira is an actual joy just like Mimi berasa sedih is an actual sadness.
Saya merasa gembira is a fundamental wellness in constant positivity.
Back to the question what is the difference between merasa and berasa.
Merasa is a constant base feeling whereas berasa is an actual feeling occuring at a particular point.
Saya berasa gembira apabila saya nampak cikgu saya.
Saya merasa gembira kerana cikgu saya sangat baik hati.
We bear in mind that such distinctions are at best an academic exercise.
The actual world sees emotion as a vague concept or experience hence
a speaker is more concerned with naming the feeling rather than identifying the various states of experiencing an emotion.