The news comes from a Smash Bros event at E3 2014, hosted by series creator Masahiro Sakurai. He pointed out (though an interpreter), that these customized moves will not be available when playing the "with anyone" mode, but you can use them when playing the "with friends" mode. Furthermore, custom characters can be transferred between the 3DS and Wii U versions of Super Smash Bros. When asked how that process would work, Sakurai told Joystiq that we'd have to wait for the Wii U release to find out.
Players will also be able to give their players "equipment" which alters certain statistics, like speed. Different characters will be able to hold different amounts of equipment, said Sakurai, noting that larger characters can hold more equipment, while lighter, more agile characters can't carry as much, to compensate for their other advantages.