What are they and how do they move your accounts?
A transfer moves from one custodian directly to another custodian. You do not see the money. The result is no tax or penalty.
A direct rollover again is custodian to custodian with you in the middle. You have a check made by the original custodian made out to the new custodian for benefit of you (FBO). The check is mailed to you and you mail the check to the new custodian. As long as the check is made out to the newcustodian, there is no problem. The result is no tax or penalty.
An indirect rollover has the original custodian making out a check to you. They will most likely withhold 20% for taxes. You have up to 60 days to get that money and the withheld money into another tax sheltered plan. If you do this with 60 days, you get the withheld money back when you file your taxes. If you don’t meet the deadline, you will look at this like a withdrawal and pay the 10% penalty if you are under 59 ½.