Actually, A/A and A/P are wrong terminology for SQL Server. I helped start that way back in the SQL Server 2000 days when I was still an employee of MS and wrote the SQL 2K failover clustering whitepaper.
The proper term is some variation of single instance failover cluster (or failover clustering instance) or multiple instance failover cluster. I've seen a variation with active in the name, I've seen where SQL Server is explicitly called out.
For SQL Server, A/P and A/A were holdovers from SQL Server 7.0 clustering where you literally could only have a maximum of two installs (and I'd rather try to block that ugliness out of my head). It makes no sense to say active/active/passive or a/a/a/a/a/p since that is probably not what it looks like. For example, you could have a three node cluster but have four instances running on two nodes. That isn't a/a/a/a/p.
When they introduced instancing in SQL Server 2000, we had talked about a name that made sense. My whitepaper was the first place to use the newer stuff and it's evolved a little over the years. Unfortunately, people are still clinging to A/P and A/A. Much like Windows clustering will always be referred to by some as MSCS. It is what it is.
Now you know ... the rest of the story.
So yes, I'm still a bit chuffed and annoyed people are using A/P and A/A. At this point it's like people spelling my name wrong (i.e. Alan, Allen). I try to ignore it but know that it is wrong terminology.
Also, N+1 comes from W2K Datacenter and you could do up to four nodes, boxes were smaller so having multiple instances were more of a challenge, and have a single dedicated failover node was a potential scenario. It evolved into N+i, where i is a number of dedicated failover nodes in the Windows failover cluster since it's easier now to have more than one dedicated failover node if you want. I believe the SQL 2K failover clustering wp was one of the first places to use that as well. That is proper use of N+i. I've never seen something like what Paul said with N-i or whatever.
PS - I won't shame anyone in a public talk if you use A/P or A/A. 🙂
PPS - I highly recommend if you want to see how complex a multiple instance topology can be, take a look at my whitepaper "Applying Updates to a Clustered Instance of SQL Server 2008 or SQL Server 2008 R2" which is linked from my blog post here[/url].