I know this is going to sound pedantic, but here goes - - -
We need to be more careful in terms that we use, and in the particular context of this thread, to differentiate between the generic names, proprietary product names, and names that vaguely apply to broad categories of products. Specifically:
Linseed oil, Tung oil, and Walnut oil are specific types of oils. All are derived from plants and are categorized as 'drying oils' in that they will eventually (some faster than others) combine with oxygen to 'polymerize', or cure to a hard, plastic-like finish. Linseed oil may also be called 'flax seed oil' because it is extracted from flax, the plant that produces the fiber used to make linen. There is a special version of Linseed oil called 'Boiled Linseed Oil', or BLO, that is specifically treated to make it cure faster. The name is derived from the fact that originally the treatment involved heating the raw oil, but today is a matter of adding chemical compounds (often heavy metal compounds involving cadmium or chromium) that achieve the same effect.
Tru-Oil is the name of a proprietary product made by one manufacturer. It is a blend of Linseed oil, Stoddard solvent (basically, less-flamable form of mineral spirits), and other unidentified proprietary oils. Similarly, other proprietary product names include AussieOil, OsmoOil, etc.
Teak Oil is a generic marketing name for a finish intended for outdoor application that may include Linseed oil, Tung oil, mineral oil (a byproduct of petroleum refining), and any number of other additives. It is NOT made from Teak, but rather the name was derived from its original use as a finish for items made of teak wood.
Danish oil is a generic name for blends of oils (including Linseed oil, Tung oil, various oils derived from safflower and sunflower seeds, etc), solvents (typically, mineral spirits but possibly turpentine or other solvents), and in some cases, varnish solids. There are as many different formulas for Danish Oil as there are manufacturers making it. Strictly speaking, Teak oil and Tru-Oil could be categorized as Danish oils.
And then there are oil products that also contain wax - the 'hardwax oils', and proprietary products such as Howard's Feed n Wax, and even some of the Teak Oils. Also, there are products that include oils or waxes derived from animals rather than plants - for example, Neetsfoot Oil is a leather preservative based on components extracted from cattle.