Both are standard. Which one produced the figure is stated with it.
Calendar days, not trading days. Implied volatility is quoted on calendar time and the contract decays over a weekend.
Annualized, as quoted.
A normal distribution places about 68% of outcomes inside one standard deviation and about 95% inside two.
The band is symmetric in dollars around the price entered, spanning 1 standard deviation over 30 calendar days.
Hypothetical illustration, computed only from the figures entered. Every input is typed; nothing here reads a live quote or a chain.
The volatility route linearizes a lognormal price around the spot, so the band is symmetric in dollars while a price is not, and a wide band can place its lower bound below zero. The straddle route uses the square root of pi over two, which follows from the at-the-money straddle formula at a zero rate and yield. Neither states a direction, and an implied volatility is a price rather than a measurement of what will happen.
Option prices carry a view on how far the underlying travels before expiry. Converting a quoted implied volatility, which is an annual figure, into the move over the actual days left gives the one-standard-deviation band the options are priced against. The at-the-money straddle answers the same question directly, because its price is what the round trip costs.
A $100 underlying with 30% implied volatility and 30 calendar days to expiry has a one-standard-deviation move of $8.60, or 8.601%, so the band runs $8.60 either side of the $100 price. The at-the-money straddle on those inputs prices near $6.86, about 0.80 of that move, so the straddle route multiplies by about 1.25 to get back to it.
Reading the straddle price as the standard deviation. It is about 80% of it, so taking it at face value understates the band by a fifth.