System comprising - an energy storage module of a first type for use with an electrical device in the form of an electrical hand-operated power tool or a suction unit wherein, on a mounting area of a module casing of the energy storage module, there are provided a device interface with plug-in interlocking contours for attaching to plug-in mating interlocking contours of an energy storage interface of the electrical device along an insertion axis, together with electrical contacts (63, 64) for making contact with electrical mating contacts (33, 34) of the energy storage interface of the electrical device to create an electrical connection of the energy storage module and the electrical device, which make electrical contact (63, 64) with one another during plug-in fitting of the device interface to the energy storage interface, wherein the energy storage module has at least one energy store mounted in the module casing, in particular an assembly with at least one rechargeable electrical storage cell, for the provision of electrical power at the contacts (63, 64), wherein the mounting area is provided at a plug-in projection for insertion in a plug-in socket of the energy storage interface of the electrical device, and the electrical contacts (63, 64) are arranged on a side wall section of the plug-in projection extending along the insertion axis, characterised in that has - an energy storage module of a second type, which has an energy store for the provision of electrical power to the contacts of its device interface, which corresponds to the device interface of the energy storage module of the first type, together with a module casing, in particular cubic, with a side face on which the fixing device is provided, so that the energy storage module of the second type may be attached with the side face to the side of an electrical device, and the module casing protrudes from a device casing of the electrical device with a section facing away from the sie face. - an energy storage module of a first type for use with an electrical device in the form of an electrical hand-operated power tool or a suction unit wherein, on a mounting area of a module casing of the energy storage module, there are provided a device interface with plug-in interlocking contours for attaching to plug-in mating interlocking contours of an energy storage interface of the electrical device along an insertion axis, together with electrical contacts (63, 64) for making contact with electrical mating contacts (33, 34) of the energy storage interface of the electrical device to create an electrical connection of the energy storage module and the electrical device, which make electrical contact (63, 64) with one another during plug-in fitting of the device interface to the energy storage interface, wherein the energy storage module has at least one energy store mounted in the module casing, in particular an assembly with at least one rechargeable electrical storage cell, for the provision of electrical power at the contacts (63, 64), wherein the mounting area is provided at a plug-in projection for insertion in a plug-in socket of the energy storage interface of the electrical device, and the electrical contacts (63, 64) are arranged on a side wall section of the plug-in projection extending along the insertion axis, characterised in that has - an energy storage module of a second type, which has an energy store for the provision of electrical power to the contacts of its device interface, which corresponds to the device interface of the energy storage module of the first type, together with a module casing, in particular cubic, with a side face on which the fixing device is provided, so that the energy storage module of the second type may be attached with the side face to the side of an electrical device, and the module casing protrudes from a device casing of the electrical device with a section facing away from the sie face.