the feeling of being certain that something exists or is true;
a strong feeling that something is true or real;
Belief is a feeling of certainty that something exists, is true, or is good.
great trust or confidence in something or someone;
strong belief in God or a particular religion;
If you have faith in someone or something, you feel confident about their ability or goodness.
Since I have faith in dictionaries (not belief), from the definitions I got, my belief (not faith) is that when we consider certainty of IDEAS we use belief and when something is mainly related to CONFIDENCE in SOMETHING or SOMEONE we use faith.
The idea transacted by 'belief in God' must be the certainty in its existence + faith.
And the idea transacted by 'faith in God' must be the confidence in God.
'Belief in Buddhism' implies the certainty in its truth or goodness + faith.
"My family still believes in God; but after this pandemic I lost faith in Him." Without any explanation if this statement conveys the same idea as intended, the second part of the sentence is to filter out faith (confidence) from belief. That means, in some occasions belief can contain faith (confidence in something) also [without any scientific evidence].
Often neither of these words can be replaced by the other. So we can say, one is not a subdivision of the other.