docs(common): term/definition updates

docs/initialization.md

@@ -43,3 +43,7 @@ const instance = await createInstance(SepoliaConfig);
 The information regarding the configuration of Sepolia's FHEVM and associated Relayer maintained by Zama can be found in the `SepoliaConfig` object or in the [contract addresses page](https://docs.zama.ai/protocol/solidity-guides/smart-contract/configure/contract_addresses).
 The `gatewayChainId` is `10901`.
 The `chainId` is the chain-id of the FHEVM chain, so for Sepolia it would be `11155111`.
+
+{% hint style="info" %}
+For more information on the Relayer's part，please refer to [the Relayer SDK documentation](https://docs.zama.org/protocol/relayer-sdk-guides).
+{% endhint %}

docs/input.md

@@ -1,7 +1,7 @@
 # Input registration
 
 This document explains how to register ciphertexts to the FHEVM.
-Registering ciphertexts to the FHEVM allows for future use on-chain using the `FHE.fromExternal` solidity function.
+Registering ciphertexts to the FHEVM allows for future use onchain using the `FHE.fromExternal` solidity function.
 All values encrypted for use with the FHEVM are encrypted under a public key of the protocol.
 
 ```ts

docs/public-decryption.md

@@ -1,10 +1,8 @@
 # Public Decryption
 
-This document explains how to perform public decryption of FHEVM ciphertexts.
-Public decryption is required when you want everyone to see the value in a ciphertext, for example the result of private auction.
-Public decryption can be done using the Relayer HTTP endpoint.
+This document explains how to perform “public decryption” of FHEVM ciphertexts. Here, public decryption means decrypt-to-public. It is required when you want everyone to be able to see the value contained in a ciphertext, for example, the result of a private auction. Public decryption can be performed using the Relayer HTTP endpoint.
 
-## HTTP Public Decrypt
+## HTTP public decrypt
 
 Calling the public decryption endpoint of the Relayer can be done easily using the following code snippet.
 
@@ -33,6 +31,6 @@ const handles = [
 const results: PublicDecryptResults = instance.publicDecrypt(handles);
 ```
 
-## Onchain Public Decryption Verification
+## Onchain public decryption verification
 
-For more details about public decryption and on-chain decryption proof please refer to the on [public decryption page](https://docs.zama.ai/protocol/solidity-guides/smart-contract/oracle).
+For more details about public decryption and onchain decryption proof please refer to the on [public decryption page](https://docs.zama.org/protocol/solidity-guides/smart-contract/oracle).