A number of warbler species have two different primary song types, one to attract mates and another to defend territories. The former is sung early in the season by unmated males, less after pairing up, more during the day, more in the center of the territory, and usually in repeat mode (same song sung over and over). The latter is more commonly performed later in the season, is sung more often at dawn and at the edge of territories, is heard during male-male interactions, is often more complex, often has chipping in between phrases, and is often sung in serial mode by those species with larger repertoires.
In the literature these songs are variously called accented/unaccented, type 1/type 2, type A/type B, first/second category, early/late, common/varied, territorial/nesting, repeat/mixed mode etc. The classification of these two different song types varies between and even within species, depending on whom you read.
An example of the confusion: In the Black-throated Green Warbler, the type A song is the territorial song to ward off males, the Type B song the one used to attract females. The two song types are reversed in the Golden-cheeked Warbler, a close relative of the Black-throated Green: Type A is the one used near females, type B to maintain territory.
Another example: the group B songs of the Prairie Warbler in the BNA account are type A songs in the recent Warbler Guide (Stephenson and Whittle). This is not an error, just a difference in the basis of classification (contextual vs structural).
In addition to their inconsistent use, the terms type A and type B are non-descriptive and convey no information about context.
The often used accented/unaccented terminology only works for a few species, and whether or not a song is accented is often difficult to determine. Additionally, in some species accented songs are used both for attracting mates and in maintaining territory, as in Blackburnian and Yellow Warblers. The terms can't be applied to the Black-and-white Warbler, where no song is accented, the dawn song being longer and more complex than the unaccented day song, or in the Pine Warbler, where the dawn song is the repertoire sung in serial mode, while during the day the same songs are sung in repeat mode.
Most of the other descriptive classifications have not been widely used.
In my opinion the two best options are first/second category and dawn/day. First category for the intersexual and second category for the intrasexual songs was recommended by Spector in his superb analysis of warbler song, and has often been utilized.
In his book Birdsong by the Seasons Don Kroodsma describes the territorial song of the Blackburnian Warbler as the dawn song and the female attraction song as the day song. The dawn/day classification is descriptive and immediately conveys to me the function of the song type, even though the dawn song phrases may be heard during the day, and vice versa. This is a simple means of classifying the two song types, that anyone can understand, that can be applied to most of these species of warbler, and is applicable to many other families such as the flycatchers, sparrows, tanagers, thrushes and parids (even though their song systems may not be homologous).
There is one situation where the classification gets a bit tricky. In a few species such as Hooded, Chestnut-sided and Yellow, the second category song phrases sung in serial mode at dawn can be sung in repeat mode during the day. These are still second category song phrases, and the song is still presumably intrasexual, but the mode as well as the timing has changed. These songs would be more accurately named second category unless they were in serial mode, in which case they would represent dawn songs sung during the day.
So to conclude, my vote is to call the intersexual female attraction song the first category or day song, and the intrasexual territorial song either the second category or the dawn song, the song type being identifiable either by the phrases used and/or by their mode and time of delivery. I think these terms should be used universally in published studies. Any terminology that leads to consistency across all the warbler species that have two song categories would be a much needed improvement.
Note: Some species of warbler, mostly those that sing only one song, have an additional song type, the flight song.
Some examples of dawn songs:
Pine Warbler at dawn, phrases same as day but sung in serial mode.
songs spliced together
Blackburnian Warbler at dawn, with chipping between second category phrases, not heard in first category day songs. Note:phrases are accented, unlike most second category songs.
Hooded Warbler dawn song, singing unaccented second category phrases in serial mode. During the day, accented (first category) or unaccented (second category) songs are sung in repeat mode.
Black-and-white Warbler at dawn, singing more complex phrases than the day song.
Spector, D. A. 1992. Wood-warbler song systems: A review of paruline singing behaviors. Curr. Ornithol. 9:199-238.
Bolsinger, J. S. 2000. Use of two song categories by Golden-cheeked Warblers. Condor 102:539-552.
Birdsong by the Seasons. Donald Kroodsma, Houghton Mifflin, 2009.
The Warbler Guide. Tom Stephenson and Scott Whittle, Princeton University Press, 2013.
The Birds of North America Online (BNA). Cornell Lab of Ornithology and American Ornithologists Union.