When I touch and hold the app I want to delete, nothing comes up for me to delete it. Is there another way I can delete an app?

There are some iOS and iPadOS apps which cannot be deleted.

Here are the built-in apps which can be deleted:

Delete built-in Apple apps from the Home screen on your iOS 14 or iPadOS device or Apple Watch - Apple Support

Which app are you trying to delete?

The press-and-hold should place all apps into “jiggle mode”.

The following would be what is expected on iOS and iPadOS 14 (14.4), with holding an icon.

The other way to delete is the X that appears when a deletable app is long-pressed. That looks like this:

If your iPhone or iPad is managed by or provisioned by someone or some group such as an IT support group, that can prevent the removal of specified apps.

Above assumes the apps being targeted for deletion are deletable apps—all add-on apps are, and many of the iOS and iPadOS apps are, but not all. See the link in my previous reply.

I can't seem to delete any 3rd party apps. Holding down app does not give option to delete, just remove.