The integral flanges are defined by that solid extension at the back of the flange called tapered hub. Other "flanges" and hub assemblies are considered integral if sufficient full penetration weld is uniting the flange and hub. The only weld may be considered to give integral quality is the full penetration weld, refer Figures 2-4. The loose flanges show fillet weld of the "hub" to the pipe / nozzle neck. That is not considered strong enough for integral flange qualification. Refer also to the Clause 2-4(a)(1) definition of the loose flange.
When in doubt of the strength of the weld joining the flange end hub, design it as loose flange, but if you opt to design it as integral flange and it breaks in operation, it's your neck ...
Sketch 4(a);- if the weld on the back of the flange in sketch 4(a) looks like the weld on the back of the flange in sketch 8, then it can be designed as integral flange. Otherwise, the fillet weld in the back of the flange of sketch 4(a) will qualify only for the name of loose flange.
The sketch 7 shows a welded flange assembly resembling the sketch 5, which in turn resembles the forged "long weld neck flanges" and the like. It is also explained in the Clause 2-8(a)(1)(a) "...integral type [Fig. 2-4 sketch (7)] where the neck material constitutes the hub of the flange;"
Phew, it takes some sweat to select the correct words to explain the old cook book and I'm still not sure of it. I suggest you, to sit down and read carefuly every page, clause, note and flange detail on the sketches, then chew on it a few days, it will dawn on you one day and you'll be happy.