“Vascular plants” will correspond to...

[Daniel Madzia]

Actually, it's quite possible that, under the PhyloCode, [...] "vascular plants" will correspond to "Apo-Tracheophyta", which [...] Tracheophyta reserved for the crown group.

Cantino & Donoghue in Cantino et al. (2007) defined “Tracheophyta” as follows: “The most inclusive crown clade containing Zea mays L. 1753 (/Spermatophyta) but not Phaeoceros laevis (L.) Prosk. 1951 (Anthocerotophyta) or Marchantia polymorpha L. 1753 (Marchantiophyta) or Polytrichum commune Hedw. 1801 (Bryophyta).” So, you're right that “Tracheophyta” is [most likely] reserved for the crown clade, but it doesn't mean that Tracheophyta (or tracheophytes) is not the same as vascular plants. At least it is in Cantino et al. (2007) where it's clear that the term “vascular plants” refers to the crown group Tracheophyta (although they introduced “Apo-Tracheophyta” as well). A good topic for discussion, though.

Reference
Cantino, P. D., Doyle, J. A., Graham, S. W., Judd, W. S., Olmstead, R. G., Soltis, D. E., Soltis, P. S. & Donoghue, M. J. 2007. Towards a phylogenetic nomenclature of Tracheophyta. Taxon 56: 822–846.

[keesey]

Thanks for linking to that paper.

Their definition of Apo-Tracheophyta is, "The most inclusive clade exhibiting tracheids (i.e., differentially thickened water conducting cells) synapomorphic with those in Pinus sylvestris L. 1753." If you equate vascularity with the possession of tracheids, then this is the clade corresponding to the descriptive phrase "vascular plants", not the more exclusive crown group Tracheophyta. Apparently, though, the known composition is not very different, if different at all -- they mention rhiniopsids as possible non-tracheophyte apo-tracheophytes, but it depends on whether, "tracheids with S-type and G-type cell walls (see Kenrick & Crane, 1997: Fig. 4.26) are homologous."

Incidentally, I looked up images of Rhiniopsida and they look charmingly cladogram-like. See, e.g., the illustration of Cooksonia at Palaeos Paleozoic: Devonian: The Devonian Period - 2 (Plants), or this one from Wikimedia Commons:

[David Marjanović]

Yep. Instead of "dendrograms", let's talk about "rhyniograms" or "cooksoniograms"...

Phylogeny and morphology of the earliest land plants seems to be a very active area of research right now; a couple of surprises have already come out, like... Rhynia or Cooksonia (I forgot which) actually had its sporangia next to the terminal buds, not instead of them, and tracheids may have evolved twice, and (an old idea) the megaphyll almost certainly evolved lots of times, and...