What cable do I need to connect a late 2014 iMac to an external monitor?

Note that the article linked above on TDM does not apply if you want to use a free-standing external monitor instead of another iMac. This article covers free-standing ones:

Use external monitors with your Mac - Apple Support

There is a link in that article to another that helps you find what cabling is required.

To connect a Mini DisplayPort monitor to a late 2014 iMac you need a Mini DisplayPort cable. A Thunderbolt cable won't work, even though the plugs will fit. The Thunderbolt 2 ports on the iMac will work with a Thunderbolt or Mini DisplayPort cable, but a monitor's Mini DisplayPort won't work with a Thunderbolt cable.

Apple Thunderbolt Cable (2.0 m) - White - Apple

"The Apple Thunderbolt Cable lets you connect a Thunderbolt-equipped system to a Thunderbolt device."

Apple doesn't make Mini DisplayPort cables.

The Apple Thunderbolt 2 cable should work for that: Apple Thunderbolt Cable (2.0 m) - White - Apple

The older iMac must be a 27" 2009 or 2010 model or any iMac from 2011 through 2014 only.

See here: link-> Use your iMac as a display with target display mode - Apple Support

Not necessarily. The only reason for a Mini-DisplayPort to Mini-DisplayPort is if the external monitor also has a Mini DisplayPort connector.

I use a Mini-DisplayPort to HDMI adapter-cable. (Apple sells a premium Belkan 4K rated version here). Alternatively a Mini-DisplayPort to standard DisplayPort might work even better if your monitor supports the second.

Malcolm J. Rayfield wrote:

To connect a Mini DisplayPort monitor to a late 2014 iMac you need a Mini DisplayPort cable. A Thunderbolt cable won't work, even though the plugs will fit. The Thunderbolt 2 ports on the iMac will work with a Thunderbolt or Mini DisplayPort cable, but a monitor's Mini DisplayPort won't work with a Thunderbolt cable.

Apple Thunderbolt Cable (2.0 m) - White - Apple

"The Apple Thunderbolt Cable lets you connect a Thunderbolt-equipped system to a Thunderbolt device."

Apple doesn't make Mini DisplayPort cables.

This is not entirely accurate.

While the TB2 cable can be used to connect Mini Display port devices to a TB2 equipped Mac. The reverse is what is not possible, connect TB2 devices to a Mini Display Port equipped Mac.

TB2 includes the Mini Display port signal, so can be used with Mini Display Port devices. There is no reason for the TB2 cable to not work in this scenario, since it will be the Display / Monitor that will depetermine what signal it gets from the port and the TB2 cable is perfectly capable of carrying either signal or both.

See: https://blog.startech.com/post/what-you-need-to-know-about-thunderbolt-vs-mini-displayport/

The 20-pin Thunderbolt 2 port on a computer does include Mini DisplayPort signals.

https://connector.pinoutguide.com/20_pin_Apple_Thunderbolt/

But see the note at the bottom of the Thunderbolt version

https://pinoutguide.com/SerialPorts/apple_thunderbolt_pinout.shtml

"The Thunderbolt cable has five wires: one for management and two uni-directional pairs, one for incoming and second for outgoing traffic."

In the link you posted

https://blog.startech.com/post/what-you-need-to-know-about-thunderbolt-vs-mini-displayport/

look in the "What works, what doesn’t?" section.

"The image below shows which combinations of Thunderbolt (TB Cable) and Mini DisplayPort (DP Cable) will (green) and will not (red) work together."

http://blog.startech.com/wp-content/uploads/2015/05/TB_vs_MDP.jpg

It shows Thunderbolt cables not working with non-Thunderbolt displays.

Here is Apple talking about connecting a Thunderbolt Mac to a Mini Display port display (in this case a 2009 or 2010 iMac in Target Display Mode).

About Thunderbolt to Thunderbolt cable (2.0 m) - Apple Support

"Although a Thunderbolt cable will fit into Mini DisplayPort connections, only Mini DisplayPort cables can be used in Target Display Mode with an iMac (Late 2009) or iMac (Mid 2010) connected to a Thunderbolt-enabled Mac"

https://eshop.macsales.com/blog/10899-target-display-mode-and-thunderbolt

"DisplayPort iMacs require a DisplayPort cable, though they can work with either DisplayPort or Thunderbolt Macs.

Only get a Thunderbolt cable if you’re going to connect two ThunderBolt-equipped computers together, it won’t work for anything else."

https://mike952.wordpress.com/2011/07/21/thunderbold-and-minidisplay-mac-compatibility-101/

"MBA Thunderbolt iMac 27″ Mini Display Mini Display Cable Worked Fine

MBA Thunderbolt iMac 27″ Mini Display Thunderbolt Cable Did Not Work"

https://www.startech.com/en-us/faq/displayport-mdp-and-thunderbolt "Note: When you connect a Thunderbolt source to a Mini-DisplayPort display, you must use a Mini-DisplayPort cable."

https://blog.tripplite.com/whats-the-difference-between-thunderbolt-and-mini-displayport

"And while a Thunderbolt-enabled computer can connect to a DisplayPort monitor, the technology of the cable needs to match the technology of the display."

"And why doesn't apple make a Mini DisplayPort cable if their older computer used them?"

Apple's Mini DisplayPort displays had permanently attached cables with Mini DisplayPort plugs, so Apple didn't need to sell Mini DisplayPort cables.

Yes. Thunderbolt and Displayport use the same port type. And Thunderbolt contains the Display Port signal within it.