Wikipedia:
Conceptual Model
A mental model captures ideas in a problem domain, while a conceptual model represents 'concepts' (entities) and relationships between them. Conceptual modelling is a well known technique of data modelling, together with logical modelling and physical modelling.

Note that term 'logical modelling' [sic] does not have an associated page. Why not ? Perhaps they are using a more restricted sense of conceptual modeling as part of data modeling that was popular in the 1980s and 90s.

Formulating a more rule-based definition, a conceptual model is a mental model used for formal knowledge representation problems, including 'logical modeling' which often gets mixed up with 'logical database modeling'. The mention of data and physical modeling in the definition above is something of a red herring.

Model (Abstract)
Modeling Language
Conceptual Schema
Concept Map
Conceptual Framework

Category - Scientific Modeling
Scientific modelling is the process of generating abstract, conceptual, graphical and or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling.

Probably closer to a rule-based definition of 'conceptual modeling'. Note the section for Types of Scientific Modeling.

Category - Conceptual Systems
Conceptual System
A conceptual system is a system that is comprised of non-physical objects, i.e. ideas or concepts. In this context a system is taken to mean "an interrelated, interworking set of objects".

Though somewhat skimpy, this definition may be nearer to a more inclusive and modern use of term conceptual modeling.

Fox Wiki:
Conceptual Modeling
Conceptual Modeling is the process of capturing and documenting the requirements of a system. There are several methods for capturing a Conceptual Model. Each method varies in its degree of formallity. The more formal the method, the easier it is to transform it into an implementation.
... Conceptual models portray applications at a fundamental level, using terms and concepts familiar to the application users. In contrast, logical and physical models specify underlying database structures to be used for implementation, and external models specify user interaction details (e.g. design of screen forms and reports).

Probably a better definition than Wikipedia

Category - Modeling
Conceptual Model
A Conceptual Model describes the design of an application from the perspective of the owners and/or users of the application. Since a conceptual model does not focus on implementation it is inherently more stable than a Logical Model or Physical Model.

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