From the Super Mario Wiki
Grand Tail Goombas are a sub-species of Grand Goombas that have been given Tanooki tails that debut in Super Mario 3D Land.
Super Mario 3D Land
Like normal Tail Goombas, they move by leaping into the air, hovering to another area close to them, then swinging their tails upon landing; however, because they are larger than the average Goomba, their tail swing attack covers a larger radius. They are not much bigger than normal Goombas, though, due to their size being cut down to fit the 3DS screen.
They first appear in World 1-1, but seldom appear after that. Grand Tail Goombas give the player three coins when defeated, and in World 5-5, one gives the player a Super Leaf.
Mario & Luigi: Dream Team
In Mario & Luigi: Dream Team, Grand Tail Goombas are found in Dreamy Neo Bowser Castle. In this game, they are referred to as Big Tail Goombas. They do not show up on the map.
In battle, the large Goombas have two attacks, the first of which consists of them hovering towards Mario, which would need to be countered with a hammer, and may cause dizziness if not.
The second of the attacks consists of them spinning on the ground in a semi-homing pattern towards Mario. Mario can move out of the way, or jump over the Big Tail Goomba in this attack. If the Goomba strikes another foe, it does damage to the other foe. The Goomba may also themselves get dizzy, signified by a more violent spin. This will cause them to sit for a second in front of Mario when they near him, and then simply walk towards.
Names in other languages
||Gran Goomba Tanuki (M&L: Dream Team)
||Big Tanooki Goomba