My question involves a child custody case from the State of: california

I have a 3 year old little boy. me and my son live in cali and his father lives in tx. his father is not on the bc and i have full legal custody. his father hasnt tried to visit him. he didnt send him anything for his birthday or christmas. he doesnt pay child support. and he sends texts saying he hopes me and our son have a great life. ad saying i dont want anything to do with our son. and my son was on his insurance but took him off and said wanted nothig to do with him. then a couple days later he texted again and said i am coming to cali and i better be scared and he is coming for our son. that was in january then yesturday i got a text saying i will see you in july which idk what he means but probably to take me to court. i know there are different types of custody and visitation. i just want to know all the types of full custody, joint custody and visitations. could what he text me about not wanting anything to do with him affect him getting any custody. and i just think he would get visitation while i get full custody. just cuz i think he is only going after visitation and not want custody but i would still like the difference. nothing has been filed yet i just want to get inform about all the custody and visitation options.