Update "Intro to Mojo & Services" documentation to the new mojo types

Small update to change the remaining bits of the documentation that
were still showcasing the old mojo types, instead of the new ones.

Bug: 955171
Change-Id: I1f5ebfcdda5c933b3728713fa622c8fdf4270eb8
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1978661
Reviewed-by: Oksana Zhuravlova <oksamyt@chromium.org>
Commit-Queue: Mario Sanchez Prada <mario@igalia.com>
Cr-Commit-Position: refs/heads/master@{#726866}
diff --git a/docs/mojo_and_services.md b/docs/mojo_and_services.md
index 2950004..52a5957 100644
--- a/docs/mojo_and_services.md
+++ b/docs/mojo_and_services.md
@@ -613,12 +613,13 @@
 // to most service interfaces.
 service_manager::Connector* connector = content::GetSystemConnector();
 
-// Recall from the earlier Mojo section that mojo::MakeRequest creates a new
-// message pipe for our interface. Connector passes the request endpoint to
-// the Service Manager along with the name of our target service, "math".
-math::mojom::DividerPtr divider;
-connector->BindInterface(math::mojom::kServiceName,
-                         mojo::MakeRequest(&divider));
+// Recall from the earlier Mojo section that BindNewPipeAndPassReceiver()
+// creates a message pipe and yields a PendingReceiver as its return value.
+// Connector passes the receiver endpoint to the Service Manager along with
+// the name of our target service, "math".
+mojo::Remote<math::mojom::Divider> divider;
+connector->Connect(math::mojom::kServiceName,
+                   divider.BindNewPipeAndPassReceiver());
 
 // As a client, we do not have to wait for any acknowledgement or confirmation
 // of a connection. We can start queueing messages immediately and they will be
@@ -627,8 +628,8 @@
     42, 6, base::BindOnce([](int32_t quotient) { LOG(INFO) << quotient; }));
 ```
 *** aside
-NOTE: To ensure the execution of the response callback, the DividerPtr
-object must be kept alive (see
+NOTE: To ensure the execution of the response callback, the
+mojo::Remote<Divider> object must be kept alive (see
 [this section](/mojo/public/cpp/bindings/README.md#A-Note-About-Endpoint-Lifetime-and-Callbacks)
 and [this note from an earlier section](#sending-a-message)).
 ***
@@ -646,7 +647,7 @@
 example, the `Divide` call would never reach the `math` service (in fact the
 service wouldn't even be started) and instead we'd get an error message (or in
 developer builds, an assertion failure) informing us that the Service Manager
-blocked the `BindInterface` call.
+blocked the `Connect` call.
 
 ## Content-Layer Services Overview