Both! It does both!!!

FullOuterPowerShellJoin.ps1

$ThingsILike = 'Coffee', 'Whiskey', 'Food', 'ToMoveItMoveIt' | ForEach-Object -Process {
    [PSCustomObject]@{
        Name = $_
    }
}
$ThingsICanDrink = 'Coffee;$true', 'Whiskey;$true', 'Food;$false', 'Ice;"...um...both?"' | ForEach-Object -Process {
    $Name, $CanDrink = $_ -split ';'
    [PSCustomObject]@{
        Name     = $Name
        CanDrink = $CanDrink
    }
}
$JoinParams = @{
    Left              = $ThingsILike
    Right             = $ThingsICanDrink
    LeftJoinProperty  = 'Name'
    RightJoinProperty = 'Name'
    Type              = 'AllInBoth'
    Prefix            = 'InRight_'
}
Join-Object @JoinParams