I noticed that I can create application links to our JIRA Server in two different locations in crucible.
Directly in the Projects menu of the crucible administration or when I click on the gear wheel next to the repositories.
Are those two different types of app-links or just two ways to do the same thing?
From your description, I believe you're actually referring to Project Links, which are links that can be created between a JIRA project and a Crucible project or repository, if an Application Link between the applications is already created.
Although the option to create them is still present, they were mostly used in the past and we do not recommend their usage anymore, as there are no real benefits from using them in most recent versions of JIRA and Crucible, and also because they should be deprecated in the future.
Still, just out of curiosity, please allow me to link you to some old documentation about them, so you can have an idea about what they used to serve for:
The new Development Integration Plugin, which is responsible for the management of the Development Panel in JIRA (the portion in a JIRA issue which shows information from your developer tools) isn't affected by Project Links, which is why I mentioned they are not actually used anymore. They were actually used by the old JIRA FishEye Plugin.