In archeological and paleontological terms, ancient is just a term meaning very old. Usually things older than the fall of the Roman Empire and the start of more modern cultures that still exist today. For example, we have ancient species that still exist, such as plants and animals.
In your terms, I think hey mostly would call those evolutionary ancestors. For example, we usually call earlier evolutions "early horse", or better yet, by their actual names, Mesohippus, etc, as they're not true horse.
An ancient horse is just as accurate here, as it is for mummified horses in Ancient Egypt -- only 3,000 - 4,000 years old. Or for example, a extinct form of Gibbon found in a noblewoman's tomb in Ancient China.
In general I think Ancient refers to having been along the lines of human Evolution. Before that is pre-history stuff, and usually with unique terminology, such as relating to an era in time, like paleo to paleolithic.
A way to really mess with it's use is when they apply Ancient to male king bees, as in terms of life-span, 6 months is insane.