If you're going to be in this business then you should spend some time learning the nomenclature, which is at least half of all understanding. To help you on your way, in the world of typography, that flavor of typeface** is called a 'script'. There is a small subset of scripts that is sometimes called 'handwritten' but your sample of LHF Sarah Script is not one of them.
**The proper term here is 'typeface', not 'font'. A font is a specific incarnation of a typeface, a specific size, weight, condensed/regular/extended, italics or not, etc.
this clears it up. I like the last line that says in a nutshell it is like the difference between a song and an album.
"Does It Even Matter Anymore?
Even among type professionals, there's a growing acceptance that for most people, the terms font and typeface can be used interchangeably. Only experts really need to worry about it.
"For most people in most situations, those terms can swap around without any trouble," Tobias Frere-Jones tells Co.Design. "The distinction would matter in type design, obviously, but also contexts which involve engineering, like app development or web design."
Gary Hustwit, director of Helvetica, agrees. "Most people other than type designers just say 'font,'" Hustwit says. "Among graphic designers, though, I'd say it's a generational thing. A lot of the older designers I've met, like Massimo Vignelli, always say 'typeface.'"
And Pentagram's Eddie Opara puts it even more succinctly: "I think it's the latter, a distinction for experts," he says. "I know it certainly pisses experts off."
In A Nutshell
Even type experts agree: Typeface and font can be used interchangeably at this point. But if you come across an annoying pedant who cares deeply about maintaining the distinction for the masses, just remember this: The difference between a font and a typeface is the same as that between songs and an album. The former makes up the latter. Remember that and you're good to go."