A battery, comprising: a casing including cells housed therein; and a terminal part including a connection terminal connected to an electrode terminal (61, 95) of a connection apparatus, wherein the casing includes a front face and a rear face which are positioned on opposite sides in a longitudinal direction, two side faces which are positioned between the front face and the rear face in a widthwise direction orthogonal to the longitudinal direction, and a top face and a bottom face which are positioned between the front face and the rear face and between the two side faces in a height direction orthogonal to both the longitudinal direction and the widthwise direction, wherein, in the casing, a first functional groove and a second functional groove are formed on both sides of the terminal part in a widthwise direction, each functional groove having an identifying function for identifying a type of the connection apparatus in which the longitudinal direction coincides with a connection direction of the connection terminal and the electrode terminal (61, 95), wherein each functional groove includes a first functional unit and a second functional unit, wherein the first functional unit and the second functional unit are continuously formed in a widthwise direction and have different length, and the first functional unit is positioned on a further center side in the widthwise direction than the second functional unit, and wherein a face of the second functional unit continuous to the first functional unit in the widthwise direction is formed as an inclining face which is displaced to the bottom face side as the face approaches the side face positioned on an opposite side to the first functional unit, wherein the first functional unit has a rectangular shape and the second functional unit has a triangular prism shape, wherein two notches are formed in the casing, each notch is formed in the casing by a level difference face which is continuous to one side face and a groove forming face which is continuous to the bottom face, wherein two guided grooves are formed in the casing, each guided groove is opened to one groove forming face and the front face, and wherein a face positioned to be closest to the rear face side among faces forming the functional grooves is positioned on a further front face side than a face of each guided groove which is positioned to be closest to the rear face side. a casing including cells housed therein; and a terminal part including a connection terminal connected to an electrode terminal (61, 95) of a connection apparatus, wherein the casing includes a front face and a rear face which are positioned on opposite sides in a longitudinal direction, two side faces which are positioned between the front face and the rear face in a widthwise direction orthogonal to the longitudinal direction, and a top face and a bottom face which are positioned between the front face and the rear face and between the two side faces in a height direction orthogonal to both the longitudinal direction and the widthwise direction, wherein, in the casing, a first functional groove and a second functional groove are formed on both sides of the terminal part in a widthwise direction, each functional groove having an identifying function for identifying a type of the connection apparatus in which the longitudinal direction coincides with a connection direction of the connection terminal and the electrode terminal (61, 95), wherein each functional groove includes a first functional unit and a second functional unit, wherein the first functional unit and the second functional unit are continuously formed in a widthwise direction and have different length, and the first functional unit is positioned on a further center side in the widthwise direction than the second functional unit, and wherein a face of the second functional unit continuous to the first functional unit in the widthwise direction is formed as an inclining face which is displaced to the bottom face side as the face approaches the side face positioned on an opposite side to the first functional unit, wherein the first functional unit has a rectangular shape and the second functional unit has a triangular prism shape, wherein two notches are formed in the casing, each notch is formed in the casing by a level difference face which is continuous to one side face and a groove forming face which is continuous to the bottom face, wherein two guided grooves are formed in the casing, each guided groove is opened to one groove forming face and the front face, and wherein a face positioned to be closest to the rear face side among faces forming the functional grooves is positioned on a further front face side than a face of each guided groove which is positioned to be closest to the rear face side.