As explained below, Axe and Mace are considered separate weapons. See Axe and Mace, Weapons#Axe and Weapons#Macebr>
In Combinations, they combine differently. See Axe Combinations and Mace Combinations
However, they share one set of Break Arts. See Axe and Mace Break Arts
Axes and Maces are very similar in use; chopping and hammering are similar actions with different effects. They both have short handles. They are lumped together in the ingame item description. Their Tiers intersect; the damage leapfrogs in early Tiers. They are given one set of Break Arts between them. This has lead some guides to group them together in Combinations tables.
However, in these guides, different weapons being called Designs, the Axe Design and the Mace Design are separate.
Axe and Mace Combinations follow the patterns of different-Design Combinations and do not follow the patterns of same-Design Combinations; in these significant ways, they are different Designs for the purposes of Combinations. Every other two weapon Designs have combinations between weapons of different Tiers that 'devolve' the higher Tier into the same Design of a lower Tier than either weapon; this, axes and maces do. Every other two weapons of the same Design of consecutive Tiers will create the next consecutive Tier; axes and maces do not, with rare exceptions.