Since near-term at-the-money (ATM) options are generally the most liquid, the listed implied vol for a stock is usually pretty close to the nearest ATM volatility, but there's not a set convention that I'm aware of.
Also note that for most stocks, vol skew (the difference in vol between away-from-the-money and at-the-money options) is relatively small,
correct me if I'm wrong, IV is the markets assessment that the stock is about 70% likely (1 Standard Deviation) to move (in either direction) by that percent over the next year.
Not exactly. It's an annualized standard deviation of the anticipated movements over the time period of the option that it's implied from. Implied vol for near-term options can be higher or lower than longer-term options, depending on if the market believes that there will be more uncertainty in the short-term. Also, it's the bounds of the expected movement in that time period. so if a stock is at $100 with an implied vol of 30% for 1-year term options, then the market thinks that the stock will be somewhere between $70 and $130 after 1 year. If you look at the implied vol for a 6-month term option, half of that vol is the range of expected movement in 6 months.