This is one of the main areas of interest in semiotics and as such, it's vastly covered, although there are 2 main theories from which posterior theories emerge. These theories have more than 100 years and are the theoretical support for modern design, starting from first wave of linguistics , then Bauhaus and coming to these days.
To make it short, these theories were created by Ferdinand de Saussure (dyadic sign model) and Charles Peirce (triadic relation theory):
There are two major theories about the way in which signs acquire the
ability to transfer information; both theories understand the defining
property of the sign as being a relation between a number of elements.
In the tradition of semiotics developed by Ferdinand de Saussure the
sign relation is dyadic, consisting only of a form of the sign (the
signifier) and its meaning (the signified). Saussure saw this relation
as being essentially arbitrary, motivated only by social convention.
Saussure's theory has been particularly influential in the study of
linguistic signs. The other major semiotic theory developed by C. S.
Peirce defines the sign as a triadic relation as "something that
stands for something, to someone in some capacity"1 This means that
a sign is a relation between the sign vehicle (the specific physical
form of the sign), a sign object (the aspect of the world that the
sign carries meaning about) and an interpretant (the meaning of the
sign as understood by an interpreter). According to Peirce signs can
be divided by the type of relation that holds the sign relation
together as either icons, indices or symbols. Icons are those signs
that signify by means of similarity between sign vehicle and sign
object (e.g. a portrait, or a map), indices are those that signify by
means of a direct relation of contiguity or causality between sign
vehicle and sign object (e.g. a symptom), and symbols are those that
signify through a law or arbitrary social convention.
While both theories cover your specific question, the triadic relations model relates to it in a more direct manner. See below the description or classes of triadic signs:
- by what stands as the sign — either (qualisign, also called a tone) a quality — or (sinsign, also called token) an individual fact — or (legisign, also called type) a rule, a habit;
- by how the sign stands for its object — either (icon) by its own quality, such that it resembles the object, regardless of factual connection and of interpretive rule of reference — or (index) by factual connection to its object, regardless of resemblance and of interpretive rule of reference — or (symbol) by rule or habit of interpreted reference to its object, regardless of resemblance and of factual connection; and
- by how the sign stands for its object to its interpretant — either (rheme, also called seme,such as a term) as regards quality or possibility, as if the sign were a qualisign, though it can be qualisign, sinsign, or legisign — or (dicisign, also called pheme, such as a proposition) as regards fact, as if the sign were an index, though it can be index or symbol — or (argument, also called delome) as regards rule or habit. This is the trichotomy of all signs as building blocks in an inference process.
- Any qualisign is an icon. Sinsigns include some icons and some indices. Legisigns include some icons, some indices, and all symbols.
- Any icon is a rheme. Indices (be they sinsigns or legisigns) include some rhemes and some dicisigns. Symbols include some rhemes, some dicisigns, and all arguments.
An easy example
Linguistics and specifically theory of signs is a very dense subject, so I'd understand if you didn't read the explanation above. So let me use a real life example:
We were building an sciences app for students covering different subjects, two of them being Hydrography and Oceanography. Being this for teens, it was clear any iconography used had to be extremely clear and simple, so we started using wavy lines to represent the significant for river, streams of water, and hydrography by association. It worked somehow, just not enough to consider it 100% effective (not even close). Regarding oceanography, we chose "sea like" waves and a version with a lighthouse as well. None of them worked as satisfactory as we would hope.
Then we tried a few more options until we came with a helm and a starfish for both concepts. Amazingly, they did the trick. While we are used to this kind of associations and a helm wasn't really far fetched, we were vey curious as to why they chose helm for river and a starfish for sea. The answers were in the line of "obviously a starfish is from sea" and "starfish is for sea, so helm has to be for river".
This is to illustrate how significants work in triadic models. The icon wasn't direct, most kids never saw a helm and probably they never saw a real starfish. Yet, the connection between significants (including context) was strong enough to provide the most accurate results. And the same happens with your examples: there's no need for a real connection between significant, signifier and interpretant , these connections are artificially created by context, culture, technology, reference groups and so on.
A phone shape is not a phone, but the collection of signifiers the interpretant derives from that shape in a given context