There is now a canonical document on DNS terminology:
RFC 8499 aka BCP 219
Here are its relevant definitions, slightly abridged and reordered:
"Recursive resolver: A resolver that acts in recursive mode. [..] [RFC4697] tried to differentiate between a recursive resolver and
an iterative resolver."
"Recursive mode: A resolution mode of a server that receives DNS
queries and either responds to those queries from a local cache or
sends queries to other servers in order to get the final answers
to the original queries."
"Iterative resolution: A name server may be presented with a query
that can only be answered by some other server. The two general
approaches to dealing with this problem are "recursive", in which
the first server pursues the query on behalf of the client at
another server, and "iterative", in which the server refers the
client to another server and lets the client pursue the query
there. (See Section 2.3 of [RFC1034].)
In iterative resolution, the client repeatedly makes non-recursive
queries and follows referrals and/or aliases. The iterative
resolution algorithm is described in Section 5.3.3 of [RFC1034]."
The RFC 4697 quoted above says this:
This memo is concerned principally with the behavior of iterative
resolvers, which are typically found as part of a recursive name
server. This memo uses the more precise term "iterative resolver",
because the focus is usually on that component. In instances where
the name server role of this entity requires mentioning, this memo
uses the term "recursive name server". As an example of the
difference, the name server component of a recursive name server
receives DNS queries and the iterative resolver component sends
queries.
RFC 1034 seems to me even more unclear on this, or more precisely even more outdated:
- In any system that has a distributed database, a particular
name server may be presented with a query that can only be
answered by some other server. The two general approaches to
dealing with this problem are "recursive", in which the first
server pursues the query for the client at another server, and
"iterative", in which the server refers the client to another
server and lets the client pursue the query. Both approaches
have advantages and disadvantages, but the iterative approach
is preferred for the datagram style of access. The domain
system requires implementation of the iterative approach, but
allows the recursive approach as an option.
Back to your question of:
What it is the difference between iterative and recursive DNS from a caching point of view?
In my understanding on how things work in the wild (which is not exactly aligned with the definitions above), there are no differences as a recursive nameserver does iterative queries to resolve whatever names the client has asked for.
and for
Can the local DNS server still take a shortcut in a recursive architecture?
Basically anything not being authoritative can have a cache, and as long as it obeys the TTLs it got from previous replies it received, it is working inside the bounds of the protocol.
Note that in the future things may get more muddy: some proposals like ANAME
and specific implementations may require an authoritative nameserver to also become recursive/iterative at the time a given query comes in order to be able to resolve the target.