Pin flower of Primrose.
The single style is the only organ seen since that is much longer than the shorter and therefore obscured stamens.
Thrum flower of Bird's-eye Primrose.
The (five in this case) stamens are the only organ seen since they are much longer than the shorter and therefore obscured style.
The flowers of Primrose are heterostylous, meaning that there are two flower types, the pin (aka longistylous) form and the thrum (aka brevistylous) form. The two forms are sexually mutually exclusive - either form can only fertilise the opposite form - they are said to exhibit heteromorphic self-incompatibility where two flowers of the same morph are unable to fertilise one another, presumably including themselves. Thus only pollen from long stamens can pollinate long styles, and only pollen from short stamens can pollinate short styles, it is more than just a case of one being hidden because it is shorter, they are genetically incompatible with each other. Self-incompatibility is controlled by genes. Cross-pollination creates genetic diversity and is more beneficial for the survival and evolution of the plant than one that can pollinate itself.
Flowers having either of these two morphs are called distylous. There are but few distylous plants. Examples include many Primula species such as Primrose and Bird's-eye Primrose (Primula farinosa), a few species of Linum such as Cultivated Flax (Linum usitatissimum) and the non-native (Linum hirsutum). This small sub-set is fairly surprising given the apparent evolutionary advantage imposed upon plants possessing this characteristic. But maybe heterostyly is just an evolutionary stepping stone to plants being fully-blown Dioecious, where a plant has either all male or all female flowers, which also increases genetic biodiversity. Perhaps
Primrose and Flax didn't quite take the atrophy of one or other of the sex organs to the full extent, and didn't actually become dioecious, but rather are in a half-way-house stage.
Not all heterostylous flowers have one or other of the style or stamen hidden, the only requisite is that two forms exist; one where the stamen is longer than the style, and another where it is vice versa. For instance, in Cultivated Flax the style and stamens visibly protrude out into the open.
Because the pin and thrum forms are determined by genes, the same plant has either all pin flowers or all thrum flowers rather than a mix of both forms (your Author thinks).
In the WildflowerFinder website, the following icons are used:
Pin form of heterostyly
Thrum form of heterostyly
There exist also plants which are tristylous, having three differing morphs. The three morphs are the result of the two organs having three differing lengths, short, medium and long (rather than only two as with distylous):
In the first the style is short and the stamens are long and medium.
The second has the style medium length and the stamens long and short.
In the third the style is long and the stamens short and medium.
Examples of plants that are tristylous are
Bermuda Buttercup (Oxalis pes-caprae), Purple Loosestrife (Lythrum salicaria) and some other species of Lythrum.