Exactly right. The class you mention is originally known as a functor with the operator parenthesis.
And very notably though, lambdas are slightly more efficient. Because no class is truly constructed. The constructor you wrote is not actually called - it can be optimized out by the compiler. There is no constructor/destructor just copying capture values and invocation of the () method and of course the object is stack constructed not dynamically allocated.
A really thorough analysis is here:
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https://web.mst.edu/~nmjxv3/articles/lambdas.html
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Useful conclusions:
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1. Functors and lambdas are always passed a this pointer, whereas plain functions naturally are not. This consumes an extra register and 8 bytes of stack space.
2. Lambda "constructors" are inlined into the function in which the lambda is created. This significantly reduces the amount of copying performed (2 instructions for lambdas, 5 for functors), as well as avoiding a function call setup and teardown.
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