In short, services set to Automatic will start during the boot process, while services set to start as Delayed will start shortly after boot.
Starting your service Delayed improves the boot performance of your server and has security benefits which are outlined in the article Adriano linked to in the comments.
Update: "shortly after boot" is actually 2 minutes after the last "automatic" service has started, by default. This can be configured by a registry key, according to Windows Internals and other sources (3,4).
The registry keys of interest (At least in some versions of windows) are:
HKLM\SYSTEM\CurrentControlSet\services\<service name>\DelayedAutostart
will have the value 1
if delayed, 0
if not.HKLM\SYSTEM\CurrentControlSet\services\AutoStartDelay
or HKLM\SYSTEM\CurrentControlSet\Control\AutoStartDelay
(on Windows 10): decimal number of seconds to wait, may need to create this one. Applies globally to all Delayed services.