variable scope in functions

I have been just learning the very basics of power shell. From what I understand variables by default are private if declared in a function. I do not understand why $private:var is needed. are the following two functions equivalent in what they do?

function test {
    $a = 6 }

function test2 {
    $Private:a = 6}

take a look at this example:

function test1 {
    $a = 6
	write-host "test1: $a"
	function inner1 {
		write-host "inner1: $a"
		$a=7
	}
	inner1
	write-host "test1: $a"
}

function test2 {
    $Private:a = 6
	write-host "test1: $a"
	function inner2 {
		write-host "inner2: $a"
		$a=7
	}
	inner2
	write-host "test2: $a"
}
test1
test2

inner2 doesn’t print any value because test2 have private variable

I see functions keep stuff private from outside of them by default. To keep stuff private from functions you need the $private: syntax to accomplish this.