What's the Difference Between Yankee Gutters and Built In Gutters?
Similar or same gutters are also known as box gutters, concealed gutters, integral gutters and wooden gutters. Have I got them all? Probably not. Several sources use these terms interchangeably, several sources define each as a separate type. There are no nationally agreed upon terms but there are probably many undocumented (verbal) regionally agreed upon terms, but these regionally agreed upon terms differ from region to region.
I can't help you here. Use any term your home inspeciton client will understand.
Yankee gutters and built in gutters (and all the rest) are gutters that are a part of the of the building instead of being added on. They are not visible from the ground. You seem to be looking at a sofit.
What you need to know: Alas, although wood Yankee gutters and built-in gutters are charming they're probably rotted through from the lack of the exacting yearly maintenance that they require. A many-layer coating of roofing cement and/or a covering of roofing material or vinyl siding may very well be covering rotted pieces of lumber.
Their deterioration has also probably allowed rot of siding fascia and sofits.
There's something else: These gutters, in their almost surely rotted state, are a hazard to those of us who walk on roofs. Covered with a layer of asphalt shingles, you may forget that they're under you. Be careful.