If you send a paper bag to the landfill it’s buried in the ground (sequester), a tree is cut down to make a new paper bag, and a new tree is planted to make new material for more bags. Thus carbon is continuously captured from the air and buried deep.
If you recycle a bag then the old tree dies of old age and decomposes releasing the captured carbon back into the air. The new tree repeats the cycle, with no net carbon capture.