diff --git a/docs/index.bs b/docs/index.bs
index 5a7fd11e..3bbbe97f 100644
--- a/docs/index.bs
+++ b/docs/index.bs
@@ -1952,9 +1952,7 @@ spec: storage; urlPrefix: https://storage.spec.whatwg.org/
 
     A <dfn id="dfn-name-to-cache-map">name to cache map</dfn> is an <a>ordered map</a> whose [=map/entry=] consists of a [=map/key=] (a string that represents the name of a [=request response list=]) and a [=map/value=] (a [=request response list=]).
 
-    Each [=/storage key=] has an associated [=name to cache map=].
-
-    The <dfn id="dfn-relevant-name-to-cache-map">relevant name to cache map</dfn> is the [=name to cache map=] associated with the [=/storage key=] [=obtain a storage key|obtained=] from [=this=]'s associated [=CacheStorage/global object=]'s [=environment settings object=].
+    The <dfn>relevant name to cache map</dfn> for a {{CacheStorage}} object is the [=name to cache map=] associated with the result of running [=obtain a local storage bottle map=] with the object's associated [=CacheStorage/global object=]'s [=environment settings object=] and "<code>caches</code>".
   </section>
 
   <section>
@@ -2262,7 +2260,7 @@ spec: storage; urlPrefix: https://storage.spec.whatwg.org/
 
     The user agent *must* create a {{CacheStorage}} object when a {{Window}} object or a {{WorkerGlobalScope}} object is created and associate it with that <dfn for="CacheStorage">global object</dfn>.
 
-    A {{CacheStorage}} object represents a <a>name to cache map</a> of its associated [=CacheStorage/global object=]'s <a>environment settings object</a>'s [=environment settings object/origin=]. Multiple separate objects implementing the {{CacheStorage}} interface across documents and workers can all be associated with the same <a>name to cache map</a> simultaneously.
+    A {{CacheStorage}} object represents the [=name to cache map=] associated with the result of running [=obtain a local storage bottle map=] with its associated [=CacheStorage/global object=]'s [=environment settings object=] and "<code>caches</code>". Multiple separate objects implementing the {{CacheStorage}} interface across documents and workers can all be associated with the same [=name to cache map=] simultaneously.
 
     <section algorithm="cache-storage-match">
       <h4 id="cache-storage-match">{{CacheStorage/match(request, options)}}</h4>