Hi David:
The name "corn lily" used for Ixias no doub refer to the flowers grouped at the end of a naked stem as you see grains in wheat (the corn in this name refers to wheat and not to maize as you do in the States). Ixas are not difficult to tell as a genus on this alone. In some species the wiry stiff stems are branched but yet the whole "wheat" idea is the same. As for leaves in most species they are linear and quite narrow (in a few species broad). In very few species of Ixias the leaves are somewhat curved. Flower buds as a rule do not protrude from conspicuous bracts as they are ripening and coloring.
The character of the wiry stem is the most important one (besides the sexual organs) to tell one genus form the other.
In Tritonias as mentioned before, the flowers are not tightly clasping at the end of any wiry stem (in fact there is never a wiry stem), flowers are uniformly distributed along the stem that is mostly flexuous and as the bud ripen, they look "fat" and swollen, protruding from the bracts (that are not tiny).
As for T. lineata, some forms are clearly zygomorphic against actinopmorphic in Ixias, but there are forms of Tritonia lineata and T. parvula in cultivation that are practically actinomorphic although these could be hybrids in which a more regular form be obtained from crossing.
We have Ixia pumilio from two locations and I will try to contribute seed next spring. I have sent them in the past and they are the real thing. Again, it is a dwarf species quite different from the gems in the genus like viridiflora, monadelpha, paniculata, gloriosa, or the New Zealand hybrids.
Best
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