Difference between multiple NS and NS having multiple A

There is a semantic difference.

If an NS record (or MX record) points to a host name which subsequently resolves to multiple A (or AAAA) records these are supposed to represent alternate addresses for the same host (aka "multihoming").

See paragraphs 8 and 9 in s5.1 of RFC 5321.

Hence it's not always required that a client would try every known address for a particular host, but it should try every named host.

So, in the (normal) single-homed case with multiple name servers or mail servers, you should use a different name for each server, with a single IP, rather than one name with multiple IPs.

I suppose it just can be implementation specific - maybe some odd servers will always use only one of addresses or something like that. But normally probably should be no difference.

Btw, I found one RFC that mentions similar situation - look at RFC 2181 section 4.3, 3-rd paragraph. It says one A for one NS, but provide no reasoning.

Edit: The main difference obviously is that (1) is what everybody uses and as such 100% tested, while (2) is what nobody uses and as such there's higher possibility of it being broken is some implementations.