Does variance and standard deviation both measure how spread out the numbers are?
Yes it is. Standard deviation is a square root of variance. Square root is a monotonic transformation, meaning that it preserves the order, e.g, if a &gt; b then sqrt(a) &gt; sqrt(b), assuming a and b are non-negative and they always are for variance.

Standard deviation is easier to interpret and is more commonly used, when we calculate variance we square every term, taking a square root in standard deviation, we undo that.