In most states (primaries), people tell the pollsters who they will choose in the private voting booths, and that's what happens.
In Iowa, people knew who they intended to vote for... then they had to enter a big room and stand in a corner for that person. Then they often has to change corners if their corner wasn't big enough. Then they move around, try to convince each other, etc etc.
Everywhere else, with a primary, it'll be 'enter the booth and vote for who you want' without your religious neighbors shaking their head at you.