What is the difference between wiping polyurethane and wiping varnish?
There can be no difference, they could be the same thing. Although note that sometimes "wiping polyurethane" refers to the application method, not the product used.
What we call polyurethane or poly is a type of varnish, a fuller name for it would be polyurethane varnish although some people don't like calling it that it's perfectly accurate. Strangely given the name the polyurethane is merely an additive, actually present at quite a low level. All polys of this type are actually modified versions of an alkyd varnish, so they're technically uralkyd varnish, but uralkyd is considered an ugly word or something so it's rarely seen on labels on consumer-level packaging.
Note for anyone new to finishing: this refers to oil-based polyurethane only, not waterbased "polyurethane varnish" (which is not really a varnish in the conventional meaning of the word). The only thing they have in common is the addition of some polyurethane, they're actually completely different otherwise.
According to Bob Flexner, the only difference between this and polyurethane-based wiping varnish is that the varnish also contains linseed oil, tung oil, etc.
You've slightly misread that page. Earlier on Flexner states:
"All types of varnish are made by cooking an oil with a resin."
And lower down under Make Your Own where he says:
"After choosing a varnish, turn it into a wiping varnish by thinning it with mineral spirits."
No additional oil is needed to turn a regular varnish into a wiping varnish.
You can add more oil to a thinned varnish if you want to, but this replicates something like "Danish oil", not merely a wiping varnish. Products of the "Danish oil" type are typically said to contain approximately a 1:1:1 mixture of varnish, an oil (BLO or tung oil usually) and spirits (or turpentine if the user prefers the smell, or believes it improves its characteristics).
Can I just apply BLO to the wood and cover it with polyurethane?
Yes you can. This isn't that uncommon. The main reason you might chose to do this rather than applying the varnish directly to the bare wood is to improve the wetting of the grain, enhancing the figure in the wood (commonly referred to as "popping the grain"). Oils, on some woods, give increased contrast as well as enhancing any chatoyance (cat's eye effect) compared to the same wood with the varnish applied directly to it. On other woods there's little difference, little enough that it's often not worth the extra effort. And on others there's no difference you'd notice, except for the slightly yellower colour imparted.
This is not just a species-by-species thing, the grain in individual pieces of wood can make all the difference, so obviously this is an area where you need to do some experimentation.
But an example of where you might want to oil first is on a darker wood with good figure, such as burr walnut or ribbon-stripe mahogany, to improve contrast and maximise the chatoyance. An example of where you'd probably want to skip it is any light-coloured wood with straight grain, such as plain maple or clear white pine.