The question is indeed confusing, since it presents architectural models as if they were mutually exclusive (i.e. it can be at the same time layered and client-server) and relies on ambiguous terminology.
When it comes to architectural diagrams, there are standard diagrams, which follow a well known formal graphical notation. Typical examples are:
- UML
- Older OO notation (e.g. Booch, Rumbaugh or Objectory - it's really old because these have been merged together to make UML).
- Non OO notations, such for example the IDEF suite (which was enriched in the meantime with an OO layer), SADT, Gane & Sarson (it's also quite old, less and less used, except in some niche markets).
Among those, the only which qualifies officially and unambiguously as a standard is UML: it's the only one that is recognized by an international standard setting body (ISO/IEC 19505).
But in architecture you have also a fair bunch of non-standard diagrams that convey graphically the structural intent. Typically, a layered arrangement of services, or an hexagonal or a concentric presentations are frequently used. Sometimes it's even more visual with clients shown as PC, and several servers in the network. All these use non-standard notations.