I am not an oil expert, but this is my understanding.
First of all, yes. 4-Cycle and 4-Stroke are the same as far as internal combustion engines are concerned.
Second, the multi-viscosity rating system is a bit confusing. Yes, a 10W-30 weight oil is supposed to act like a 10 weight at low temperatures and a 30 weight at higher temperatures. The characteristics of a 30 weight at higher temperatures (100C or 212F) is well defined, but the characteristics of a 10 weight oil at low temperatures (-25C or -13F) is not. They have defined what a “10W” oil must have at these low temperatures, presumably based on what a “typical” 10 weight oil might have (the “W” in 10W is not for “weight” but for “winter”). To earn the 10W qualification, the oil must have certain viscosity and pumping characteristics at these low temperatures. To earn the “30 weight” qualification, the oil must have specific viscosity characteristics at 212F (100C).
OK, I said it was confusing. Anyway, to meet both of these ratings with the same oil, with conventional oils, they used additives that would “ball up” at low temperatures and not contribute as much to the viscosity and “unfurl” at higher temperatures to increase the viscosity when the oil got hotter. Decades ago, some oil companies used different additives which may not have compatible with each other, hence the reason for cautions about mixing oils in the engine; the result might not be as expected.
Now, introduce the synthetic oils. Instead of a mixture of long- and short-chained hydrocarbons that had a bulk viscosity that met the rating they were qualified for, they are able to produce all the hydrocarbons with the length needed to meet the viscosity rating. This also meant, with the same oil, they could meet the low temperature requirements for the 10W rating without using additives.
So, if you’ve made it this far, they are correct in their claim that it meets the requirements of both SAE 30 and 10W-30. And, no, you don’t have to worry about mixing with conventional oil. Small engines typically don’t call for a multi-viscosity oil since the low temperature rating has as much to do with pumping characteristics as it does with viscosity and many small engines do not pump the oil, but rely on the spinning parts to sling the oil where it is needed.