update terminology for clarity in customization.mdx (#4204)

Author: npentrel

src/oss/deepagents/customization.mdx

@@ -298,7 +298,7 @@ agent = create_deep_agent(
 
 <AccordionGroup>
     <Accordion title="Subagent prompts">
-        The same overlay rules apply to declarative [subagents](/oss/deepagents/subagents)—each subagent re-runs profile resolution against **its own model**, then applies the resolved profile's `base_system_prompt` / `system_prompt_suffix` to its authored `system_prompt`. The subagent's `system_prompt` plays the `BASE` role; `CUSTOM` and `SUFFIX` come from the profile that matches the subagent's model (which may differ from the main agent's profile).
+        The [prompt assembly](#prompt-assembly) overlay rules also apply to declarative [subagents](/oss/deepagents/subagents): each subagent re-runs profile resolution against **its own model**, then applies the resolved profile's `base_system_prompt` / `system_prompt_suffix` to its authored `system_prompt`. The subagent's `system_prompt` plays the `BASE` role; `CUSTOM` and `SUFFIX` come from the profile that matches the subagent's model (which may differ from the main agent's profile).
 
         | `spec["system_prompt"]` | profile `base_system_prompt` (`CUSTOM`) | profile `system_prompt_suffix` (`SUFFIX`) | Final subagent system prompt |
         | ----------------------- | :-------------------------------------: | :---------------------------------------: | ---------------------------- |
@@ -307,12 +307,12 @@ agent = create_deep_agent(
         | authored                |                    ✓                    |                     -                     | `CUSTOM`                     |
         | authored                |                    ✓                    |                     ✓                     | `CUSTOM` + `SUFFIX`          |
 
-        There is no `USER` segment for subagents—the spec's authored `system_prompt` is the closest analog and stays in the `BASE` slot. A profile that ships only a `system_prompt_suffix` (the common case for built-in Anthropic / OpenAI profiles) just appends to whatever the subagent author wrote; a profile that sets `base_system_prompt` will *replace* the authored prompt outright, so reach for that field deliberately.
+        There is no `USER` segment for subagents. The spec's authored `system_prompt` is the closest analog and stays in the `BASE` slot. A profile that ships only a `system_prompt_suffix` (the common case for built-in Anthropic / OpenAI profiles) just appends to whatever the subagent author wrote. A profile that sets `base_system_prompt` will *replace* the authored prompt outright.
     </Accordion>
     <Accordion title="General-purpose subagent prompt">
-        The auto-added [general-purpose subagent](/oss/deepagents/subagents#the-general-purpose-subagent) follows the same overlay rules with one extra layer: the GP base prompt is resolved as **`general_purpose_subagent.system_prompt` (if set) -> `HarnessProfile.base_system_prompt` (if set) -> SDK GP default**. The profile suffix layers on top either way.
+        The auto-added [general-purpose subagent](/oss/deepagents/subagents#the-general-purpose-subagent) follows the [prompt assembly](#prompt-assembly) overlay rules with one extra layer: the GP base prompt is resolved as **`general_purpose_subagent.system_prompt` (if set) -> `HarnessProfile.base_system_prompt` (if set) -> SDK general-purpose default**. The profile suffix layers on top either way.
 
-        The two override fields can both carry a base-prompt replacement, but they are not interchangeable. `general_purpose_subagent.system_prompt` is GP-specific configuration; `base_system_prompt` is a global override that primarily targets the main agent. When both are set, the **GP-specific intent wins for the GP subagent** so a user tuning both fields never sees their GP override silently dropped:
+        The two override fields can both carry a base-prompt replacement, but they are not interchangeable. `general_purpose_subagent.system_prompt` is general-purpose-specific configuration; `base_system_prompt` is a global override that primarily targets the main agent. When both are set, the **general-purpose-specific intent wins for the general-purpose subagent** so a user tuning both fields never sees their GP override silently dropped:
 
         ```python
         register_harness_profile(
@@ -332,7 +332,7 @@ agent = create_deep_agent(
         | Main agent | `"You are ACME's support orchestrator." + SUFFIX` |
         | GP subagent | `"You are a research subagent. Cite sources." + SUFFIX` |
 
-        If `general_purpose_subagent.system_prompt` is unset, the GP subagent falls back to `base_system_prompt` (when set) and finally to the SDK GP default.
+        If `general_purpose_subagent.system_prompt` is unset, the GP subagent falls back to `base_system_prompt` (when set) and finally to the SDK general-purpose default.
     </Accordion>
 </AccordionGroup>