What is the difference between Bodhayna Amavasai and Amavasai? Whys is amavasai tharpanam not performed on the day of Bodhayana amavasai? Kindly clarify why this differs during certain months.

Among the followers of Yajur Veda, a section practices the rules of Bodhayana sutram while another section follows the rules of Apasthamba sutram.
The respective followers of these two sutrams must perform amavasai as per the prescribed sutras.
One can identify the sutra they belong to from the lineage. Abhivadana mantra also contains the sutra name for the respective followers.
The amavasai prescribed by Bodhayana is slightly different. It is said even when amavasi presents in the afternoon on a given day, amavasai can be performed on that day. There are many other details involved in the calculation which we can look into this in detail later.
The followers of these two sutras must perform amavasai as per rules prescribed by these two traditions.
Notes
Amavasai tharpanam is also a shraddham. Shraddham must be performed on the day when the major portion of amavasai exists during the afternoon time. Hence, followers of Apastamba tradition (sutra) perform shraddham on the days when amavasai continues to exist during the afternoon period.
The day before Chandra darsana is Bodhayana amavasai