From the Super Mario Wiki
Bull's-Eye Bills, formerly known as Missile Bills, are heat-seeking variants of Bullet Bills typically fired from Bull's-Eye Blasters. They attack by homing in on the player. Prior to New Super Mario Bros. Wii's introduction of the current Search Killer (サーチキラー), which eventually became known in English as Bull's-Eye Bill, earlier games gave the homing abilities to normal Bullet Bills or their behavioral or color variations, as various sources treat them as. Following the introduction of their modern iteration, whenever Bullet Bills do not home in on Mario, Bull's-Eye Bills usually appear along them for that purpose.
Super Mario series
Super Mario Bros. 3
Missile Bills are introduced in Super Mario Bros. 3. In this game, a Missile Bill turns around once if it misses its target, but continues going forward without turning around after missing twice. In the original version, the colors a Missile Bill flashes are dependent on the palette the player character uses, as they cycle between all four palettes currently used on their graphical layer. As such, playing as Frog Mario or any of the normal-colored versions of Luigi causes them to flash green, while playing as Hammer Mario or Luigi causes them to flash white with bright orange arms. In the remakes, they consistently flash between black, orange, and red, while having tan-tinted arms unlike the Bullet Bill's yellow-tinted ones. Missile Bills only appear in World 4-5.
Super Mario Sunshine
Mario-seeking Bullet Bills known as Purple Bullet Bills appear in Super Mario Sunshine at Pinna Park's beach. As their name implies, they are purple with a blinking red nose, and are shot from the Monty Mole's cannon. They always home in, meaning that Mario must dodge out of their way to outrun them, since they often take several seconds to turn around. They are required to break open the baskets on the beach which hold Blue Coins. Purple Bullet Bills explode when they make contact with an object, or if Mario squirts water at them. During the final battle, Bowser Jr. sends a derivative known as Guided Bullet Bills.
New Super Mario Bros. Wii
Missile Bills appear in New Super Mario Bros. Wii. Despite having the same name of the flashing Bullet Bills of Super Mario Bros. 3 in the Prima Games guide, their Japanese name indicates that this game is the first one to use its modern iteration. They resemble normal Bullet Bills, but when one sees Mario, it will make a beeping noise and start flashing red. Here, they have a similar attack pattern to the one they had in Super Mario Bros. 3; however, in this game they can change the angle they are flying at and will not stop pursuing the player until they are defeated, or the player has gotten far enough away. They can be defeated the same way as normal Bullet Bills. They only appear in World 9-3, alongside Mario-seeking Banzai Bills referred to as King Bills.
New Super Mario Bros. U
In New Super Mario Bros. U, the Missile Bills of New Super Mario Bros. Wii make a comeback, appearing only during the Roy Koopa battle at the Rock-Candy Mines. They are seen being shot out of Roy's Bullet Bill cannon. In this case, though, after some time unsuccessfully chasing Mario, it self-destructs like a Flame Chomp.
Super Mario Maker series
Bull's-Eye Bills reappear in Super Mario Maker, Super Mario Maker for Nintendo 3DS, and Super Mario Maker 2. As they did not appear in the original Super Mario Bros. and Super Mario World, new sprites were created for those two game styles.
While they do operate similar to their appearances in New Super Mario Bros. Wii, the Bull's-Eye Bills in these games do not turn as sharply, and they will only chase after Mario for a limited time period, instead of relentlessly pursuing him.
In Super Mario Maker 2, they are replaced by Cat Bullet Bills in the Super Mario 3D World game style.
Super Mario Run
Bull's-Eye Bills appear in Super Mario Run, exclusively in Bullet Bill Barrage. Bull's-Eye Bills appear from the left of the screen and position themselves behind Mario if they are level with him. After a few seconds they will charge forward, whether or not Mario is in front of them. Like the similar Bullet Bill, they cannot be vaulted over.
Super Mario World 2: Yoshi's Island / Yoshi's Island: Super Mario Advance 3
Red Bullet Bills capable of following the player are unused in Super Mario World 2: Yoshi's Island; however, they do appear in Yoshi's Island: Super Mario Advance 3 in the final secret level, Endless World of Yoshis. They are fired from red Turtle Cannons and appear to make a biting motion as they fly, though this is purely for show. As they fly, they gradually slow down, eventually shrinking away in light blue and vanishing with a pop. They can be defeated by simply stomping or swallowing them; they look like regular Bullet Bills if spat back out, but they fly downwards.
This is the first game to have them be able to follow the player at any angle, due to the ones in Super Mario Bros. 3 and Super Mario Sunshine being restricted to lateral movement.
Yoshi's Woolly World / Poochy & Yoshi's Woolly World
Bull's-Eye Bills make their non-reissue debut in the Yoshi franchise in Yoshi's Woolly World and Poochy & Yoshi's Woolly World. They are made out of red wool. They can only be found in Knot-Wing the Koopa's Sky Fort, where they are launched from red Bill Blasters in the level itself, as well as during the boss fight with Knot-Wing the Koopa, where they are launched from the boss's Bill Blaster in addition to Bullet Bills.
Mario Party 9
Missile Bills from New Super Mario Bros. Wii make a comeback in Mario Party 9 in the minigame, Billistics, where they appear alongside Bullet Bills. In this game, Missile Bills make beeping radar noises. This is a way to tell if a Missile Bill is coming. Like in other appearances, Missile Bills will home in on the player, but when a Missile Bill misses, it will not turn around, similar to Super Mario Bros. 3 when a Missile Bill misses twice.
Captain Toad: Treasure Tracker
Bull's-Eye Bills first appear under their current name in Captain Toad: Treasure Tracker. Unlike standard Bullet Bills, Bull's-Eye Bills are fired from red Bill Blasters. They behave like in past games and similarly to the Cat Bullet Bills in Super Mario 3D World, homing in on Captain Toad or Toadette and chasing them.
Super Mario Run
Names in other languages