improved docs

docs/docs/developers/contracts/references/storage/private_state.md

@@ -68,7 +68,7 @@ Interestingly, if a developer requires a private state to be modifiable by users
 
 ## `PrivateMutable<NoteType>`
 
-PrivateMutable is a private state variable that is unique in a way. When a PrivateMutable is initialized, a note is created to represent its value. And the way to update the value is to destroy the current note, and create a new one with the updated value.
+PrivateMutable (formerly known as `Singleton`) is a private state variable that is unique in a way. When a PrivateMutable is initialized, a note is created to represent its value. And the way to update the value is to destroy the current note, and create a new one with the updated value.
 
 Like for public state, we define the struct to have context and a storage slot. You can view the implementation [here](https://github.com/AztecProtocol/aztec-packages/blob/master/noir-projects/aztec-nr/aztec/src/state_vars/private_mutable.nr).
 
@@ -134,7 +134,7 @@ Functionally similar to [`get_note`](#get_note), but executed in unconstrained f
 
 ## `PrivateImmutable<NoteType>`
 
-`PrivateImmutable` represents a unique private state variable that, as the name suggests, is immutable. Once initialized, its value cannot be altered. You can view the implementation [here](https://github.com/AztecProtocol/aztec-packages/blob/#include_aztec_version/noir-projects/aztec-nr/aztec/src/state_vars/private_immutable.nr).
+`PrivateImmutable` (formerly known as `ImmutableSingleton`) represents a unique private state variable that, as the name suggests, is immutable. Once initialized, its value cannot be altered. You can view the implementation [here](https://github.com/AztecProtocol/aztec-packages/blob/#include_aztec_version/noir-projects/aztec-nr/aztec/src/state_vars/private_immutable.nr).
 
 ### `new`
 

docs/docs/developers/contracts/references/storage/public_state.md

@@ -8,7 +8,7 @@ For a higher level overview of the state model in Aztec, see the [state model](.
 
 ## Overview
 
-The `PublicMutable` struct is generic over the variable type `T`. The type _must_ implement Serialize and Deserialize traits, as specified here:
+The `PublicMutable` (formerly known as `PublicState`) struct is generic over the variable type `T`. The type _must_ implement Serialize and Deserialize traits, as specified here:
 
 #include_code serialize /noir-projects/noir-protocol-circuits/src/crates/types/src/traits.nr rust
 #include_code deserialize /noir-projects/noir-protocol-circuits/src/crates/types/src/traits.nr rust
@@ -91,7 +91,7 @@ We have a `write` method on the `PublicMutable` struct that takes the value to w
 
 ## Shared Immutable
 
-`SharedImmutable` is a special type that can be read from both public and private!
+`SharedImmutable` (formerly known as `StablePublicState`) is a special type that can be read from both public and private!
 
 Since private execution is based on historical data, the user can pick ANY of its prior values to read from. This is why it `MUST` not be updated after the contract is deployed. The variable should be initialized at the constructor and then never changed.
 
@@ -101,6 +101,10 @@ Just like the `PublicMutable` it is generic over the variable type `T`. The type
 
 You can find the details of `SharedImmutable` in the implementation [here](https://github.com/AztecProtocol/aztec-packages/blob/#include_aztec_version/noir-projects/aztec-nr/aztec/src/state_vars/shared_immutable.nr).
 
+:::info
+The word `Shared` in Aztec protocol means read/write from public, read only from private.
+:::
+
 ### `new`
 
 Is done exactly like the `PublicMutable` struct, but with the `SharedImmutable` struct.