Christian apologetics is when people try to explain and defend their beliefs about God and Jesus to others who may not understand or agree with them. They try to answer questions and show evidence to support what they believe in.
Research Ministry is a group of people who do research about Christianity and other religions to help people understand their beliefs better. They look at different ideas and opinions from different perspectives to make sure they have all the facts before they make a conclusion. They also try to explain things in a way that everyone can understand.
So Christian apologetics and Research Ministry both work together to help people understand Christianity and its beliefs, and to provide answers to questions people may have about those beliefs.