Hiya Rob -
In the strictest sense of the term, a "climbing saw" would be one that is specifically designed for use in a tree. Some typical features would include a top handle (allowing for one-handed use), built-in lanyard ring, relatively small size (around 35 cc.), light weight (8-9 lbs.), 14" bar and 3/8" low-profile chain. Typical models would be the Stihl MS200T/020T, MS191T, and MS192T, Husqvarna 335 (junk in my opinion, but not because it's a Husky), and the Echo CS-300 and CS-340. I would say that by far the most widely used and highly regarded saw in this category is the Stihl MS200T, which replaced the 020T.
That said, a more general interpretation of the term "climbing saw" would include any make and model of chain saw that you might see a tree guy using in a tree. For many years, I climbed exclusively with a Husky 242XP with an 18" bar and .325 chain. What a little pocket rocket that thing was, OMG. The 18" bar allowed for extra "reach", and of course, capacity. I now climb with the MS192T. (As I've mentioned in other threads, my saw collection was significantly reduced when some cretin stole my Stihl 046, 036, MS200T and the Husky 242, along with my Echo PB750 backpack blower and Echo PPT-2400 power pole pruner). I'll replace the Husky 242 with the 346 (also with an 18" bar and .325 chain), and eventually get another MS200T (great saw).
I know of guys who regularly climb with larger saws than that, but they're in the minority. One guy told me he climbs with a Stihl 036, and I've heard of Husky 357's, Stihl 028's, and others. The biggest saw I ever had to use in a tree was my Stihl 066 with a 42" bar, on two different occasions. One involved a large silver maple with a 21' circumference, with leaders that were trees themselves; the other, a huge dead ash. Not recommended; I'm lucky I still have my legs.
As for the term "limbing saw": that covers a lot more ground, but to me, it just means any saw that you'd feel comfortable with (on the ground) for cutting up smaller stuff, or cutting branches off the trunks of trees; hence, "limbing". Examples might be the Stihl MS260, 280/028, 290/029, maybe your MS310, or even an MS361. In Husky, it might be a 346XP, 359, 365, or 357XP. Of course there are many, many more makes and models that could be called "limbing saws".
To specifically answer your question about what saw might complement your current "big dog", the 310, I'd say maybe the MS260 Pro, MS210 if you want to go a little smaller, a top-handled Echo maybe just for kicks, or any other Stihl, Husky or Echo that floats your boat. I pretty much just look at the specs and see what seems to make sense for what you need a saw to do. That's how I ended up getting my first Stihl 066. One look at the specs (91.6 cc, 7.0 bhp, 16.3 lbs.), and I said to myself "yeah, that'll do some damage". And it does. /forums/images/graemlins/cool.gif
That's it for now - take care, John
