Interesting question because it sort of assumes the person naming the feature was correct. First a few things about drylines:
-- Drylines don't have to be in a trof of low pressure. When an airmass mixes out from west to east on a hot afternoon the discontinuity between air masses may be gradual. Also, the associated wind shift from the dry to the more tropical (moist Mt) air may be a gradual veering shift. This happens where there is no well defined surface trof and the moisture gradually thins out with height further west. These systems are lousy to chase by the way.
-- The next type is where the air masses are separated by a trof extending south from a surface low. During the day heat, vertical mixing and westerly momentum (after the BL inversion breaks) combine to create dry air and westerly winds west of the trof axis, most common.
-- Finally, the case where the (so called) dryline is actually a Pacific front (very common) and it's mislabeled a dryline. That said, a weak continental airmass may heat and mix during the day becoming a dryline. Still, I often see Pacific frontal systems mislabeled drylines (I tend to bang on some of my forecaster friends for doing this). Why this distinction is important is another topic, but the cross sectional cut of the two do look different and the storms may form differently.
Finally in the case of your question, dryline vs trof. I think this is common especially during the early morning when dew points west of the trof axis have yet to mix out. For example, 50's Td's in the Texas Panhandle mixing down to the mid 30's by afternoon. Some people would not call the 50+ Td airmass a dryline because technically it has yet to form. Finally a dryline, a good one, is commonly defined within surface trof wind shift axis, so either is correct, but being more specific the term dryline would be best.
I'm trying to give the short and simple version here, I'll bet others will comment more on this.
Searching for the official dryline definition leads to many answers and just as many opinions. Like this one for recognizing a dryline on a synoptic map. Dryline definition: dew point contrasts of 15 degrees or more in 100 miles and a recognizable non-frontal surface wind confluence zone. This is closer to what I was characterizing in my first definition. The link follows......
One paper I found with Google Search studying the cross sectional area of drylines states that the discontinuity can very greatly along the boundary. In this particular instance a convergent low pressure trof separates the two air masses. In some of the definitions the word "sharp" is used to further define the boundary, others not. Looking up sources from the OU school of meteorology they stress a strong moist-dry difference across the boundary. This is a definition of a good dryline for severe weather, but not necessarily all drylines. In the early summer months over the high plains we get mix out drylines that are much less a part of a large synoptic scale. They certainly don't fit the strict definition I see for OU students, but given conditional instability, subtle convergence and strong afternoon heating a (surprise) severe storm will form.
We chasers tend to look at meteorological features in terms of severe weather. In that context sharp drylines in a well defined trof are best suited to what we study and chase. That said, in the wider meteorological view of changing air masses the term must be less restrictive. If for instance Dodge City has a 57Td at 2 PM with a south wind and two hours later they report a 35 Td with a west wind then they most likely had a dryline passage, albeit gradual over a longer time period. The same thing can be said for frontal systems where the change to a totally different air mass may come gradually.
The original dryline paper, at least the oldest one I remember studied the so called "Marifa Dryline" and it keyed more on the mix out process forming and moving the dryline. Today we look for more dynamic features such as large scale subsidence on the models. It can be argued how a dryline actually moves, by mix out, or by strong westerlies mixing down associated with an upper level system, all linked to the larger synoptic scale. I think where we differ is that I'm not looking at dryline in the strictest terms for synoptic scale severe weather, but more with regard to changing and moving air masses. This view also allows us to more accurately predict when things don't go right. Like veering winds and decreasing dewpoints in advance of the dryline-trof.
-- Drylines don't have to be in a trof of low pressure. When an airmass mixes out from west to east on a hot afternoon the discontinuity between air masses may be gradual.......... .
Going back over what I wrote, what I meant to say was a strong trof of low pressure. I didn't mean to imply no trof was present. Reading the rest of what I wrote I hope you can see that. One missing word can really change a sentence and when I answered you I didn't see that I missed that qualifier. I thought you were looking more for the stricter definition, so you are correct.