There is a slight difference in car engine oil and lawn mower engine oil.
The difference is the additives that are added to lawn mower oil which lawn mower manufactures require to be used in the Lawn mowers engine during the warranty period.
Those additives are supposed to protect the internal workings of the lawn mower engine.
However it's perfectly fine to use the same engine oil you use in your cars engine in your lawn mowers engine as long as you're not expecting to have warranty cover any damages to the lawnmower.
I've used car engine oil in my lawn mower for years because it's cheaper and have had no problems.