No they're not the same, and even the "definition" of tung and danish oil varies all over the place.
Tung oil - is from the tung nut. Pressed and filtered. Thats it. Thats tung oil, or should I say REAL tung oil. The garbage you buy at Lowes or Home Depot is not tung oil. What that is... is a petrochemical based "varnish" with some tung oil in it. Its just not the same stuff, it gives a different finish, smells like a petrochemical product, and I don't care for the stuff.
From our -sticky-
The true oils^ -- Linseed oil and tung oil, the drying oils most often used in finishing, are readily available and relatively inexpensive. These finishes are called true oils* to distinguish them from other products hyped as oil finishes and to separate them from naturally nondrying or semidrying oils used in finishes, such as soybean oil. These true oils* change from a liquid to a solid through polymerization, a process that strengthens the cured finish.
Linseed oil is available in several forms. Unrefined, it's called raw linseed oil, which is rarely used on wood because it dries so slowly. Finishers long ago discovered that by boiling the oil, the resulting product was thicker and dried more quickly. Even though linseed oil that has actually been boiled is still available -- it's called heat-treated or polymerized oil -- most of the boiled linseed oil sold these days is raw oil that has been mixed with chemical additives to speed up the drying time. For wood finishing, you should use only boiled linseed oil.
Tung oil is derived from the nuts of trees that are native to Asia but have been cultivated in other parts of the world. Tung oil is available in a pure, unrefined form and in a heat-treated or polymerized form. The heat-treating process makes the oil a bit more durable and speeds up the drying time. It also minimizes a tendency of tung oil to "frost" (dry to a whitish, matte appearance^^). Tung oil is paler in color and has better moisture resistance than linseed oil.
Both linseed and tung oils are penetrating finishes, which means they penetrate the fibers of the wood and harden. These are the easiest finishes to apply: Wipe them on, allow them to penetrate the surface of the wood and wipe off the excess with a rag. These oils are usually not built up with enough coats to form a surface film, like that of varnish or lacquer, because the film is too soft.
Varnishes -- Varnish is made of tough and durable synthetic resins that have been modified with drying oils. Labels on cans of varnish will list resins such as alkyd, phenolic and urethane, and the oils used are tung and linseed, as well as other semidrying oils such as soybean and safflower. Varnish cures by the same process as true oils -- polymerization -- but the resins make this finish more durable than oil. In fact, oil-based varnish is the most durable finish that can be easily applied by the average woodworker. Varnish surpasses most other finishes in its resistance to water, heat, solvents and other chemicals.***
Varnishes that contain a high percentage of oil are called long-oil varnishes. These include marine, spar or exterior varnishes and some interior varnishes for sale on the retail market. Long-oil varnishes are more elastic and softer than medium- and short-oil varnishes that contain a lower percentage of oil. Medium-oil varnishes comprise most interior varnishes on the market. Short-oil varnishes (also known as heat-set varnishes and baking enamels) require extremely high temperatures to dry, so they're used only in industrial applications.
The type of resin used in the varnish determines the characteristics of the finish. Alkyd varnish is the standard all-purpose interior variety with decent protective qualities. Phenolic varnish, usually made with tung oil, is predominantly for exterior use. Urethane varnish, also called polyurethane, offers a better resistance to heat, solvents and abrasions than any other varnish.
Varnish is typically applied with a brush, although a highly thinned and gelled version, called wiping varnish, can be applied with a rag.
Oil and varnish blends -- These mixtures, mostly oil with some varnish added, offer some of the best attributes of both ingredients: the easy application of true oils and the protective qualities of varnish. (Watco-brand Danish oil, teak oil and a number of other finishes fall into this category.) It's difficult to ascribe accurate protective qualities to these products because manufacturers don't usually disclose the ratio of oil to varnish. Oil and varnish blends will dry a bit harder than true oils, and the finishes will build quicker with fewer applications.
Let me at that a good number of the "so called" Danish**** oils are wax finishes. Waxes dissolved in solvent, like mineral spirits, the solvent allows the wax to penetrate. When the solvent dissolves, you have wax-in-the-wood (terrible if you're gonna ever consider a proper finish later on). You reapply the stuff, and it builds up more wax. What this does is do a bit of sealing to the wood, and give it a smooth feel and the ability to have some luster. Many of the Lowes and Home Depot type products are exactly this. Also the penetrating "oil" stains are like this, and not a proper finish (at least for a neck).
Read the whole sticky (in this section).
*not to be confused with Tru-Oil, another varnish finish
** Tung oil frosting, should not be used on cakes <gg>. If you use it on properly dried wood, in a medium to low humidity, and apply it correctly - THIN - you'll have a clear finish.
*** Which is why Warmoth says Tru-Oil is ok for warranty retention
**** Neither made from cheese, raisin, cinnamon, or blond buxomous females.