Agent Job Running as Computer Domain Account Rather than Service account
The job is running as the same identity in both cases.  This is a difference only in how the information is reported.  NT SERVICE\SQLSERVERAGENT is a least-privilege local identity used for running SQL Agent jobs.  Like other built-in local Windows identities this account can access network resources using the computer account.  So from the local point-of-view Agent is running as NT SERVICE\SQLSERVERAGENT, but from the network point-of-view it's running as the computer account DOMAIN\SERVERNAME$.

I don't know why the difference in reporting between your servers, but it's nothing to worry about.  

It looks like sp_whoisactive might get the login name directly from sys.dm_exec_sessions, which returns the domain identity of the login.  If you use the security_id to look up the session's server_principal you'll see the local identities differentiated.  eg:

select s.session_id, p.name
from sys.dm_exec_sessions s
join sys.server_principals p
  on s.security_id = p.sid