Ask Mr. Smarty Plants

This is the problem with common names.  The same common name may refer to one plant in one place or to one person; but, in another place or to another person, it will mean a completely different plant.  Here's a "for instance"—in our Native Plant Database try searching for "frostweed".  The search results in 8 plants with 8 different species names.  The one we know in Central Texas as "frostweed", Verbesina virginica (Frostweed), is not only a different species than the other seven, but it is in a different genus, as well.  There are many more examples of one common name used for several different species of plants.  That is why it is always best to use the botanical name if you are referring to a particular species of plant.  

You have already noticed the confusion between which plant is guajillo, huajillo, or huajilla.

In our Native Plant Database Acacia berlandieri (Guajillo) is also called Berlandier acacia, Thornless Catclaw, Mimosa Catclaw, Round-flowered Catclaw, Huajillla and Matoral.  It is in the Genus Acacia, i.e., it is an acacia.   USDA Plants Database gives the common name as 'guajillo'.  Texas A&M Aggie Horticulture calls it 'guajillo' or 'huajilla'.

In our Native Plant Database Havardia pallens (Tenaza) is also called Huajillo and Ape's ear-ring.  Its botanical synonym (what it was formerly known as) is Pithecellobium pallens.  You can see more synonyms and more taxonomic information on the USDA ARS-GRIN page.  It is in the Genus Havardia so it isn't an acacia; however, it does look a lot like the Acacia berlandieri.  The two plants are both in the Family Fabaceae (Pea Family) but the botanical taxonomists have seen a difference in the two that they considered significant enough to separate them into two different genera.  USDA Plants Database gives the common name as 'huajillo'.  Texas A&M Aggie Horticulture calls it 'guajilla' or 'huajillo'.

In the Manual of the Vascular Plants of Texas by D. S. Correll and M. C. Johnston (1970, Texas Research Foundation), the key separates the two species by this characteristic: 

• Acacia berlandieri:  "Stamens are free to the top of the floral cup or nearly so".  The common name is listed as 'Guajillo'. 
• Pithecellobium pallens (or Havardia pallens):  "Stamens united above the floral cup forming a tube 2-5 mm. long."  The common name is listed as 'Tenaza'.

Obviously, there are other differences.  See, for instance, the differences between the two by comparing their characteristics as listed on the Texas A&M Aggie Horticulture pages referred to above.

Just to make things worse, Robert A. Vines in his book, Trees, Shrubs and Wood Vines of the Southwest.  (1960, University of Texas Press) says that, as well as Acacia berlandieri, Acacia angustissima (Prairie acacia) is also called 'guajillo' and 'huajilla'; Acacia greggii (Catclaw acacia) is called 'huajilla'; and Havardia pallens (known in his book by the synonym, Pithecellobium pallens) is called 'huajillo' and 'guajilla'.

Guajillo, guajilla, huajillo and huajilla appear to be variations in spelling.  I checked several Spanish dictionaries for a translation for any of these words but found none.   I tried on the Internet and the only ones I found were for a guajillo (guajilla) chile or a reference to one of the trees/shrubs, usually Acacia berlandieri.

At this point, you may be sorry you ever asked the question. The takeaway is, however, that the assignment of common names to plants (or animals, for that matter) is not controlled; so, you may get several different unrelated plants bearing the same common name—or, one species of plant with several common names.   The botanical names are controlled.   They do occasionally change but you can usually find the trail of the change and know fairly well what plant you mean by using its botanical name.