No.

Does large standard deviation mean large variance?

A low standard deviation indicates that the data points tend to be very close to the mean. A high standard deviation indicates that the data points are spread out over a large range of values. ... The standard deviation is simply the square root of the variance.

What does it mean when the standard deviation is higher than the variance?

If the standard deviation is 4 then the variance is 16, thus larger. But if the standard deviation is 0.7 then the variance is 0.49, thus smaller. And if the standard deviation is 0.5 then the variance is 0.25, thus smaller.