diff --git a/Library/Homebrew/cask/cask.rb b/Library/Homebrew/cask/cask.rb
index 460918883e..28199331dd 100644
--- a/Library/Homebrew/cask/cask.rb
+++ b/Library/Homebrew/cask/cask.rb
@@ -113,16 +113,20 @@ module Cask
       @caskroom_path ||= Caskroom.path.join(token)
     end
 
-    def outdated?(greedy: false, skip_unversioned: false)
-      !outdated_versions(greedy: greedy, skip_unversioned: skip_unversioned).empty?
+    def outdated?(greedy: false, greedy_latest: false, greedy_auto_updates: false)
+      !outdated_versions(greedy: greedy, greedy_latest: greedy_latest, greedy_auto_updates: greedy_auto_updates).empty?
     end
 
-    def outdated_versions(greedy: false, skip_unversioned: false)
+    def outdated_versions(greedy: false, greedy_latest: false, greedy_auto_updates: false)
       # special case: tap version is not available
       return [] if version.nil?
 
-      if greedy
-        return versions if version.latest? && !skip_unversioned
+      if greedy || greedy_latest && greedy_auto_updates
+        return versions if version.latest?
+      elsif greedy_auto_updates && auto_updates
+        return versions if version.latest?
+      elsif greedy_latest && version.latest?
+        return versions
       elsif auto_updates
         return []
       end
@@ -137,10 +141,10 @@ module Cask
       installed.reject { |v| v == version }
     end
 
-    def outdated_info(greedy, verbose, json, skip_unversioned)
+    def outdated_info(greedy, verbose, json, greedy_latest, greedy_auto_updates)
       return token if !verbose && !json
 
-      installed_versions = outdated_versions(greedy: greedy, skip_unversioned: skip_unversioned).join(", ")
+      installed_versions = outdated_versions(greedy: greedy, greedy_latest: greedy_latest, greedy_auto_updates: greedy_auto_updates).join(", ")
 
       if json
         {
diff --git a/Library/Homebrew/cask/cmd/upgrade.rb b/Library/Homebrew/cask/cmd/upgrade.rb
index 9c0d51de33..fe4cb07402 100644
--- a/Library/Homebrew/cask/cmd/upgrade.rb
+++ b/Library/Homebrew/cask/cmd/upgrade.rb
@@ -19,8 +19,11 @@ module Cask
         [:switch, "--greedy", {
           description: "Also include casks with `auto_updates true` or `version :latest`.",
         }],
-        [:switch, "--skip-unversioned", {
-          description: "Skip casks with `version :latest`.",
+        [:switch, "--greedy-latest", {
+          description: "Also include casks with `version :latest`.",
+        }],
+        [:switch, "--greedy-auto-updates", {
+          description: "Also include casks with `auto_updates true`.",
         }],
       ].freeze
 
@@ -45,7 +48,8 @@ module Cask
           *casks,
           force:            args.force?,
           greedy:           args.greedy?,
-          skip_unversioned: args.skip_unversioned?,
+          greedy_latest: args.greedy_latest,
+          greedy_auto_updates: args.greedy_auto_updates,
           dry_run:          args.dry_run?,
           binaries:         args.binaries?,
           quarantine:       args.quarantine?,
@@ -62,7 +66,8 @@ module Cask
           args:             Homebrew::CLI::Args,
           force:            T.nilable(T::Boolean),
           greedy:           T.nilable(T::Boolean),
-          skip_unversioned: T.nilable(T::Boolean),
+          greedy_latest: T.nilable(T::Boolean),
+          greedy_auto_updates: T.nilabel(T::Boolean),
           dry_run:          T.nilable(T::Boolean),
           skip_cask_deps:   T.nilable(T::Boolean),
           verbose:          T.nilable(T::Boolean),
@@ -76,7 +81,8 @@ module Cask
         args:,
         force: false,
         greedy: false,
-        skip_unversioned: false,
+        greedy_latest: false,
+        greedy_auto_updates: false,
         dry_run: false,
         skip_cask_deps: false,
         verbose: false,
@@ -89,7 +95,7 @@ module Cask
 
         outdated_casks = if casks.empty?
           Caskroom.casks(config: Config.from_args(args)).select do |cask|
-            cask.outdated?(greedy: greedy, skip_unversioned: args.skip_unversioned?)
+            cask.outdated?(greedy: greedy, greedy_latest: args.greedy_latest?, greedy_auto_updates: args.greedy_auto_updates?)
           end
         else
           casks.select do |cask|
diff --git a/Library/Homebrew/cmd/outdated.rb b/Library/Homebrew/cmd/outdated.rb
index 20c6552ff1..6cac0f08a6 100644
--- a/Library/Homebrew/cmd/outdated.rb
+++ b/Library/Homebrew/cmd/outdated.rb
@@ -38,8 +38,11 @@ module Homebrew
       switch "--greedy",
              description: "Print outdated casks with `auto_updates` or `version :latest`."
 
-      switch "--skip-unversioned",
-             description: "Print outdated casks with `auto_updates` but no `version :latest`."
+      switch "--greedy-latest",
+             description: "Print outdated casks including those with `version :latest`."
+
+      switch "--greedy-auto-updates",
+             description: "Print outdated casks including those with `auto_updates`."
 
       conflicts "--quiet", "--verbose", "--json"
       conflicts "--formula", "--cask"
@@ -119,7 +122,7 @@ module Homebrew
       else
         c = formula_or_cask
 
-        puts c.outdated_info(args.greedy?, verbose?, false, args.skip_unversioned?)
+        puts c.outdated_info(args.greedy?, verbose?, false, args.greedy_latest?, args.greedy_auto_updates?)
       end
     end
   end
@@ -194,7 +197,7 @@ module Homebrew
       if formula_or_cask.is_a?(Formula)
         formula_or_cask.outdated?(fetch_head: args.fetch_HEAD?)
       else
-        formula_or_cask.outdated?(greedy: args.greedy?, skip_unversioned: args.skip_unversioned?)
+        formula_or_cask.outdated?(greedy: args.greedy?, greedy_latest: args.greedy_latest?, greedy_auto_updates: args.greedy_auto_updates?)
       end
     end
   end