The issues with resins and botanical names IS very confusing.
A short answer is that both are indications. 'Benzoin Siam' is best seen as a trade name for a certain type of resins. Originally it comes from Thailand (Siam being the 'old' name of Thailand), but it can come from other places, as long as it is alike the trade product mentioned.
The 'botanical' name used in trade is 'Styrax Tonkinensis', but it may be from other Styrax trees that supply an alike resin. So in general it is not a guarantee that the resin is from the Styrax Tonkinensis, but that the resin is of a certain type.
In case the resin is harvested in the wild it is even harder to make sure that the botanical origin is 'right', as it is with olibanum types, galbanum, asa foetida etc.
Also interesting is the fact that a 50% solution of Benzoin Siam resinoid in DEP, DPG or an alike solvent in many cases is refered to as Essential oil of Benzoin Siam. Even suppliers and books on aromatherapy sell / write about this, ignoring the fact that it is 50% a synthetic solvent.