The ZX Spectrum 48k originally came with no way to plug in a Joystick. So companies created their own interfaces to use, basically, Atari joysticks (and controller using the same 9-pin connector and pinouts for at least the 1 button and four directions). Additionally, some companies cloned these aftermarket interfaces for the Spectrum. So, A single interface may go by multiple names. With the +2, Sinclair corrected this, I guess, by including a joystick interface in the console based on the Sinclair Interface 2. But, they altered the pinouts so it was not directly compatible with most Atari type joysticks (Sinclair made their own Joysticks for it). Developers that chose to add support for joystick interfaces tended to include more than just one type of interface and players were required to select which one. Further confusion stems from game developers deciding what to call the interface on the title screen. There was no standard so the option "Sinclair", might mean the "ZX Interface 2", or "Sinclair Joystick", or a +2 compatible Sinclair joystick. The Sinclair ZX Interface 2 could also be called "SJS", "Sinclair Interface 2", "Interface 2", etc. "Protek" might mean the Protek adapter or it might mean the Protek adapter because Protek did more than one type. Does "Cursor Stick", mean the same thing as "Cursor Joystick" or "Keyboard"? Sometimes, yes. At least one game allows the 2 players to use two different adapters that cannot be connected at the same time. Even if they could, they's overlap so some player 2 controls would operate some player 1 controls and the reverse. At least one game required the player to chose a control option the first time the game ran and then never gave them the choice to a different one ever again. Something all of these have in common, except Timex units, is the control signals they sent were equivalent to keyboard input. However, the Kempston used the a hardware in such a way that it did not directly correspond to key presses. AGF and DK'Tronics are programmable interfaces where the user must run a program to select which keys are to be used. It can thus simulate other options including "Keyboard".

Keyboard
Kempston Interface/Kempston Joystick/TC2048 (port 0x1f: 000FUDLR)
Cursor Joysick/Protek (←5 →8 ↓6 ↑7 ·0 even bits of port 0xf7fe & 0xeffe starting at bit 4 of the first)
ZX Interface 2/Sinclair Interface 2 (Left Player, ←1 →2 ↓3 ↑4 ·5 port 0xf7fe, Right Player ←6 →7 ↓8 ↑9 ·0 0xeffe)
ZX +2 (same as Sinclair Interface 2 but required proprietary joysticks)
Protek/AGF (←5 →8 ↓6 ↑7 ·0)
Fuller Audio Box (port 0x7f: F---UDLR)
TS2068/TC2068 (uses registers of the AY-3-8912 sound chip)
AMX Mouse (edge connector)
Kempston Mouse
Sinclair Magnum Lightphaser
Magnum Light Phaser

The Multiface 1 expansion, interfaces use the Kempston standard.

Comcon Programmable Joystick Interface
This had 46 sets of pins which the user could connect to each other to select which key to press for each joystick control. Example, connect "↑" to "w" to press the W key when pressing up on the joystick.

Dk'Tronics interface used the Sinclair joysticks

Kempston Pro Joystick Interface had 3 game ports.

Cheetah Joystick Interface (a clone for another interface)

Sureshot Spectrum Joystick Interface (Kempston standard, works with any Spectrum unit)

The Multiface 1 (Kempston standard)

Spectrum 128 (Kempston standard)

Spectrum +3 (Kempston standard)

Ram Turbo Interface/Spectrum Turbo Interface Used Sinclair or Atari joysticks, ZX Interface 2 or Kempston