That is a context diff.  The wikipedia page https://en.wikipedia.org/wiki/Diff#Context_format has a reasonable history.  Short answer is context diffs appeared in 2.8BSD in 1981 and unified context diffs were posted to Usenet in 1990. Context diffs are more robust if you have made local changes (patch's "fuzz" messages), and unified are more compact version and can be more useful to see exactly before/after lines.

A comparison of the outputs follows:

; diff a.cpp.orig a.cpp
3d2
<     int size;
6c5
< : elem{new int[s]}, size{s}
---
> : elem{new int[s]}

; diff -e a.cpp.orig a.cpp
6c
: elem{new int[s]}
.
3d

; diff -c a.cpp.orig a.cpp
*** a.cpp.orig Sat Jul 25 11:37:29 2020
--- a.cpp Sat Jul 25 11:42:21 2020
***************
*** 1,9 ****
  class x {
      int *elem;
-     int size;
  public:
      x(int s)
! : elem{new int[s]}, size{s}
      {
      }
      ~x() { delete[] elem; }
--- 1,8 ----
  class x {
      int *elem;
  public:
      x(int s)
! : elem{new int[s]}
      {
      }
      ~x() { delete[] elem; }

; diff -u a.cpp.orig a.cpp
--- a.cpp.orig 2020-07-25 11:37:29.000000000 -0400
+++ a.cpp 2020-07-25 11:42:21.000000000 -0400
@@ -1,9 +1,8 @@
 class x {
     int *elem;
-    int size;
 public:
     x(int s)
- : elem{new int[s]}, size{s}
+ : elem{new int[s]}
     {
     }
     ~x() { delete[] elem; }

;