Based on the data from
Crowdsourcing, the word type
Beil seems to be the more common designation for AXE in the Alemannic language area while the morpho-lexical type
Axt is also common. However, more semantic than lexical variation is to be assumed here. Thus, in its article on
Bīel (cf.
Idiotikon under
Bīel), the Swiss Idiotikon points out the difference between
Beil and
Ax(t), which is further explained in the article on
Axt (cf.
Idiotikon under
Ax): "But mostly, this distinction is made: the axe has [a] longer handle, but [a] narrower edge, and is especially used for striking with the back". The Crowders may no longer be aware of this difference, or it may be irrelevant, since working with wood is not part of everyday life anymore. For even in standard language, a distinction can be made between an axe "tool with a narrow cutting edge and a long handle, especially for felling trees" (cf.
Duden under
Axt) and a hatchet "tool similar to an axe with a broad cutting edge and a short handle, especially for working wood and meat" (cf.
Duden under
Beil).
Attested in Old High German as
bîhal (cf.
AWB under
bîhal); it is a "German and Dutch word only". However, there are lexical equivalents in some Celtic languages, e.g., in Old Irish
bíail, biáil or Welsh
bwyall, bw(y)ell (cf.
Kluge under
Beil).
Karg-Gasterstädt, Elisabeth / Frings, Theodor (1952-): Althochdeutsches Wörterbuch. Auf Grund der von Elias v. Steinmeyer hinterlassenen Sammlungen im Auftrag der Sächsischen Akademie der Wissenschaften zu Leipzig, Lepzig
LinkSeebold, Elmar (2012): Kluge. Etymologisches Wörterbuch der deutschen Sprache, Berlin, DeGruyter