Both are "standard". The first picture as per UML specs is

Structured Activity Nodes

A StructuredActivityNode is an Action that is also an ActivityGroup (see sub clause 15.6) and whose behavior is specified by the ActivityNodes and ActivityEdges it so contains. Unlike other kinds of ActivityGroup, a StructuredActivityNode owns the ActivityNodes and ActivityEdges it contains, and so a node or edge can only be directly contained in one StructuredActivityNode. StructuredActivityNodes may be nested (as a StructuredActivityNode, as an Action, is also an ActivityNode), however, so an edge or node may be indirectly contained in a number of nested StructuredActivityNodes.

Activity Groups

ActivityGoups are a grouping constructs for ActivityNodes and ActivityEdges. Nodes and edges can belong to more than one group. This sub clause describes two concrete kinds of ActivityGroups, ActivityPartitions and InterruptibleActivityRegions. StructuredActivityNodes are a third kind of ActivityGroup, but they are also Actions and are discussed in sub clause 16.11 of Clause 16 on Actions.

The 2nd picture is

Invocation Actions

An InvocationAction is an Action that results, directly or indirectly, in the invocation of a Behavior (see sub clause 13.2). InvocationActions include the CallActions for calling Operations or Behaviors and for starting Behaviors that have been previously instantiated. Additional kinds of InvocationActions allow for the targeted sending of signals and other objects and the ability for broadcasting signals to available receivers.

The main difference between both cases is re-use. While in the first place you just have some complexity at a single place (your Pet the cat) the second one is when you (re-)use a certain action at multiple places. However, I tend to use the invocation variant even if it's only for a single use. Here I add a composite diagram (which in EA opens on dbl-click) to show details of the according action. The main flow just shows the overview and if details are needed, they are just a dbl-click away.

Now, creating a composite diagram in EA is (again) different. You need to create an AD on package level and then drag this into the invocation element. Now, when you dbl-click that, the embedded diagram will open.

While your question is a very specific one it actually winds down to a question how to represent a loop using an activity diagram. I strongly recommend checking this answer. In your case I guess the first approach from the answer is the most suitable.