Explain where the name Gym comes from; Gym Key Terminology doc is missing some of the old material

docs/about/concepts/key-terminology.md

@@ -2,33 +2,39 @@
 
 # Key Terminology
 
-Essential vocabulary for agent training, RL workflows, and NeMo Gym. This glossary defines terms you'll encounter throughout the tutorials and documentation.
+Essential vocabulary for model training, RL workflows, and NeMo Gym. This glossary defines terms you'll encounter throughout the tutorials and documentation.
 
 ## Rollout & Data Collection Terms
 ```{glossary}
 Rollout / Trajectory
-    A complete sequence of agent-environment interactions, from initial prompt through tool usage to final reward score. The complete "story" of one agent attempt.
+    A complete sequence of model, user, and environment interactions, from initial prompt through tool usage to final reward score. The complete "story" of one attempt at a task.
 
 Rollout Batch
     A collection of multiple rollouts generated together, typically for the same task. Used for efficient parallel processing.
 
+Environment
+    The conditions in which your model operates. Functionally, this typically refers to tools the model has access to.
+
 Task
-    An input prompt paired with environment setup (tools + verification). What you want agents to learn to do.
+    An input prompt paired with environment setup (tools + verification). What you want models to learn to do.
 
 Task Instance
     A single rollout attempt for a specific task. Multiple instances per task capture different approaches.
 
+Training environment
+    A set of tasks that share the same environment setup compiled into a single prompt dataset.
+
 Trace
     Detailed log of a rollout including metadata for debugging or interpretability.
 
 Data Generation Process
-    The complete pipeline from input prompt to scored rollout, involving agent orchestration, model inference, tool usage, and verification.
+    The complete pipeline from input prompt to scored rollout, involving rollout orchestration, model inference, tool usage, and verification.
 
 Rollout Collection
     The process of applying your data generation pipeline to input prompts at scale.
 
 Demonstration Data
-    Training data format for SFT consisting of input prompts paired with successful agent responses. Shows models examples of correct behavior.
+    Training data format for SFT consisting of input prompts paired with successful rollouts. Shows models examples of correct behavior.
 
 Preference Pairs  
     Training data format for DPO consisting of the same prompt with two different responses, where one is preferred over the other.
@@ -47,30 +53,30 @@ Orchestration
     Coordination logic that manages when to call models, which tools to use, and how to sequence multi-step operations.
 
 Verifier
-    Component that scores agent outputs, producing reward signals. May also refer colloquially to "training environment with verifiable rewards."
+    Component that scores rollouts, producing reward signals. The word "verifier" may also refer colloquially to a different definition: "training environment with verifiable rewards."
 
 Service Discovery
     Mechanism by which distributed NeMo Gym components find and communicate with each other across machines.
 
 Reward / Reward Signal
-    Numerical score (typically 0.0-1.0) indicating how well an agent performed on a task.
+    Numerical score (typically 0.0-1.0) indicating how well a task was accomplished.
 ```
 
 ## Training Approaches
 
 ```{glossary}
 SFT (Supervised Fine-Tuning)
-    Training approach using examples of good agent behavior. Shows successful rollouts as training data.
+    Training approach using examples of good model behavior. Shows successful rollouts as training data.
 
 DPO (Direct Preference Optimization)
     Training approach using pairs of rollouts where one is preferred over another. Teaches better vs worse responses.
 
 RL (Reinforcement Learning)
-    Training approach where agents learn through trial-and-error interaction with environments using reward signals.
+    Training approach where models learn through trial-and-error interaction with environments using reward signals.
 
 Online vs Offline Training
-    - **Online**: Agent learns while interacting with environment in real-time (RL)
-    - **Offline**: Agent learns from pre-collected rollout data (SFT/DPO)
+    - **Online**: Model learns while interacting with environment in real-time (RL)
+    - **Offline**: Model learns from pre-collected rollout data (SFT/DPO)
 ```
 
 ## Interaction Patterns
@@ -80,17 +86,17 @@ Multi-turn
     Conversations spanning multiple exchanges where context and state persist across turns.
 
 Multi-step  
-    Complex tasks requiring agents to break problems into sequential steps, often using tools and intermediate reasoning.
+    Complex tasks requiring models to break problems into sequential steps, often using tools and intermediate reasoning.
 
 Tool Use / Function Calling
-    Agents invoking external capabilities (APIs, calculators, databases) to accomplish tasks beyond text generation.
+    Models invoking external capabilities (APIs, calculators, databases) to accomplish tasks beyond text generation.
 ```
 
 ## Technical Infrastructure
 
 ```{glossary}
 Responses API
-    OpenAI's standard interface for agent interactions, including function calls and multi-turn conversations. NeMo Gym's native format.
+    OpenAI's standard interface for rollouts, including function calls and multi-turn conversations. NeMo Gym's native format.
 
 Chat Completions API
     OpenAI's simpler interface for basic LLM interactions. NeMo Gym includes middleware to convert formats.

docs/about/index.md

@@ -28,6 +28,10 @@ Embedding custom training environments directly within training frameworks is co
 - Interoperable with existing environments, systems, and RL training frameworks
 - Growing collection of training environments and datasets for Reinforcement Learning from Verifiable Reward (RLVR)
 
+:::{tip}
+The name "NeMo Gym" comes from historical reinforcement learning literature, where the word "Gym" refers to a collection of RL training environments!
+:::
+
 ## Core Components
 
 A training environment consists of three server components: