What kind of NFC-Tag is only readable in Shortcuts App?
NFC is a standardized set of protocols - so in that sense "NFC is NFC". However the standard allows for multiple types of tags (i.e. your wrist band has an NFC tag embedded in it).

Currently the standard allows for 5 different types of tags, which vary in speed, capacity, mode settings, etc. For example you can set tags to be read-only or rewritable, and some types allows you to change from read-only to rewritable and vice versa, and others do not.

On top of that, NFC tags are produced by many different companies, allowing you to pick from a huge variety of form factors (dimensions, weights, etc) in various materials.

However the reason your tag is not readable by other apps is not because of these differences, nor that iOS has quirks.

It is simply so that apps tend to limit the tags that they scan to the ones associated with that app. I.e. no need to scan any random tags, if you're only interested in very specific ones. The phone actually scans every tag, but the app filters those out it is not interested in.

The Shortcuts app allows you to use more or less any tag - so it will do just that.

Update: You have updated your question indicating the specific apps you have used. You have tried to use generic apps that should read "any" tags - and thus app specific filtering is not your problem.

However your problem is instead that on iOS 12 and prior, the system allowed apps to read only tags encoded in the NFC Data Exchange Format (NDEF). Your tag must likely is not encoded in NDEF, and thus cannot be read by those apps.

On iOS 13 that limitation has been lifted. However, app developer must change their apps to expand the types of data encodings they can read. Those app you have tried aren't updated to read the specific type of tag you have.