currently I am working on a project where two different websites are created within the same NEOS installation. To achieve this I created a site package for each website and added a new site in NEOS accordingly.
Now the problem is that the Settings and NodeTypes defined in site package 1 are also available in the website of site package 2 and vice versa.
Is it possible to make everything defined in a site package exclusive to websites created with that site package?
this is not easily possible. If they are really largely different you should rather use two installations and share some packages.
If you need them to be in one installation you can separate the Configuration by using two different FLOW_CONTEXT and putting their config into a Subcontext.
The NodeTypes cannot as easily be separated, but there is an option by making most node types abstract, create actual ones for each site and via constraints prevent the one site using the others actual node types. Not super comfortable when developing as each node type exists basically up to 3 times, but possible. So you should use a whitelisting approach there.
Configuration as NodeTypes is always present for all sites in a Neos installation. But you can use Custom NodeTypes for each Homepage Node and from that it is a matter of constraints.
Basically you create a custom Page NodeType for every site and that way you can have different sets of documents and contents in each site.