This is a much more complex question to answer than a simple yes and no.
Traditionally there are two kinds of Phoenix, namely Qing Xiang and Shu Xiang, ie fresh fragrance and ripe fragrance. Fresh fragrance refers to those varieties with distinct floral ( in the Chinese sense of the word, meaning blooming flower types of fragrance ) and fresher kinds of taste profiles. Traditionally varieties such as baxian ( eight immortals ), zilan, yulan, etc belong to this category.
Ripe fragrance refers to those varieties that are baked more deeply to render the characteristically classic Phoenix oolong type of ripen fruit, honey or baked sweet potato types of aroma and a sweeter liquor. Traditionally milan, qunti, mi xiang etc belong to this category.
The grand Phoenix oolong specialist Huang Bozi further differentiates by creating the the nut taste category ( eg xingren xiang ) and pure category ( eg zhuye dancong ).
Developments in recent decades have further given rise to more varieties, but they are basically classifiable under these categories.
The most confusing part in this concept lies not in the conceptual arena but in how certain producers and wholesalers have manipulated the idea to conveniently market their products.
I was just talking to an old producer yesterday about how some sellers deceptively put grand names on ordinary products. A big name is always a big push for anything. Buyers from all over the country lined the single lane winding road in the Phoenix region trying to get the best batches. Manipulation of concepts and facts begins there. Half finished tealeaves from all round the region come through the back doors of the farmers/producers to make up for the greater demand than volume. This is only the beginning…
The resultant condition is a market with confusing understanding of what quality a certain label represents. Certainly there is also the universal condition of a huge range of quality grade under the same variety.
As a result, there can be countless kinds of quality for one single label, e.g. Milan Xiang, in the market, all tasting differently. Which category it belongs to is but one of the many puzzles. Even some wholesalers ( or claimed farmers ) have not tasted a genuine one themselves and believe, or want to believe, what they are selling is the real one.
Such is the condition for Phoenix oolong. Similar things applies to most other teas. Manipulation of the concept and muddling of the truth works for those who control the larger share of the market and have the resources to propagate myths to their commercial advantage.
BTW, for all the time I have been working with people in the Fenghuang area, I have not heard of a Hudi Laocong. A laocong basically means an old bush. How it is best processed has nothing to do with whether it is old or not, but the cultivar.
