My older iMac shows the photos on my new iPhone 14 but when I try to download them the computer shows error messages and won’t download them

I doubt that El Capitan understands the default HEIC image format produced by the iPhone 14 models. You may be able to change this to take JPG images on the phone, though I haven't looked at mine to confirm this.

The other issue is that when you connect an iPhone 13 or 14 to a Mac, a dialog appears asking to install software to provide phone compatibility with the Finder. This is probably missing in El Capitan due to its age.

Hello!

Is iCloud Photos enabled on both devices:

Set up and use iCloud Photos - Apple Support?

What error do you see? Also, using this Apple Support article as a guide, About System Information on your Mac - Apple Support, please let us know what year your Mac is and what version of macOS you are currently using.

Jack

chesterfromasheville wrote:

My imac is a mid 2007 7.1 operating system is os x el capitan10.11.

An iMac that old certainty will have compatibility issues due to its advanced age (almost 16 years old). It is, unfortunately, obsolete. For security and compatibility, you should consider a new Mac:

Buy Mac - Apple.

Jack