Both do the same thing like forwarding the requests to appropriate name servers who are authoritative for the DOMAINS in the queries. However, there is difference in both, Stub Zone are Dynamic and Conditional forwarder are static.

Conditional Forwarding –  Where you want DNS clients in separate networks to resolve each others’ names without having to query DNS servers on the Internet, such as in the case of a company merger, you should configure the DNS servers in each network to forward queries for names in the other network. DNS servers in one network will forward names for clients in the other network to a specific DNS server that will BUILD up a large cache of information about the other network. When forwarding in this WAY, you create a direct point of contact between two networks’ DNS servers, reducing the need for recursion.

Stub Zone– Stub-Zones are dynamic -A stub zone is like a secondary zone in that it obtains its resource records from other name servers (one or more master name servers). A stub zone is also read-only like a secondary zone, so administrators can’t manually add, REMOVE, or modify resource records on it. But the differences end here, as stub zones are quite different from secondary zones in a couple of significant ways.First, while secondary zones contain copies of all the resource records in the CORRESPONDING zone on the master name server, stub zones contain only three kinds of resource records:

• A copy of the SOA record for the zone.
• Copies of NS records for all name servers authoritative for the zone.
• Copies of A records for all name servers authoritative for the zone.

Both do the same thing like forwarding the requests to appropriate name servers who are authoritative for the domains in the queries. However, there is difference in both, Stub Zone are Dynamic and Conditional forwarder are static.

Conditional Forwarding –  Where you want DNS clients in separate networks to resolve each others’ names without having to query DNS servers on the Internet, such as in the case of a company merger, you should configure the DNS servers in each network to forward queries for names in the other network. DNS servers in one network will forward names for clients in the other network to a specific DNS server that will build up a large cache of information about the other network. When forwarding in this way, you create a direct point of contact between two networks’ DNS servers, reducing the need for recursion.

Stub Zone– Stub-Zones are dynamic -A stub zone is like a secondary zone in that it obtains its resource records from other name servers (one or more master name servers). A stub zone is also read-only like a secondary zone, so administrators can’t manually add, remove, or modify resource records on it. But the differences end here, as stub zones are quite different from secondary zones in a couple of significant ways.First, while secondary zones contain copies of all the resource records in the corresponding zone on the master name server, stub zones contain only three kinds of resource records: