I have recently come across several American recipes that call for an ingredient described as 'Smoked Sausage' or 'Smoked Italian Sausage'.  Here in Australia, we try to be a little more specific, so is it a longer, skinny item like Cabanossi (Popular on pizza) or Kabanos, or one of a plethora of sausage products that are either smoked or cooked in a brine tank, or even both?  Are they short or long? Are they relatively unspiced etc, or garlicky, peppery etc? 
I can’t comment what those specific recipes mean, but based on experience here in the US, ‘smoked sausage’ is pretty generic, albeit with some relatively consistent properties. In particular, ‘American’ smoked sausage usually:  Has pork as the primary meat, and if not is usually a blend of multiple meats. Has the meat medium to finely ground. Has a ‘medium’ casing (not super soft, but still pretty easy to cut with a decent knife, and still holds together reasonably well). Is pre-cooked, not dried, and not cured. Has a rather mild flavor with little in the way of spices or herbs involved.  In theory, any sausage you can source locally that meets all those points should work fine in most American recipes that call for ‘smoked sausage’. There are two special exceptions to this:  Louisiana Cajun and Creole dishes may assume Cajun Andouille sausage due to the extremely heavy French influence on that area’s cuisine. This is similar to French Andouille sausage, though typically double-smoked and often with a heavy helping of cayenne pepper as part of the seasoning. This will usually be called out explicitly, but is not always. Some Hawaiian dishes may assume something closer to Portuguese linguiça. Portuguese cuisine had a major influence on modern Hawaiian cuisine, and this is one big way it still shows. Again, this will usually be called out explicitly, but is not always.   ‘Italian sausage’ is trickier. What most Americans think of as Italian sausage is a fresh, coarse-ground, pork sausage seasoned primarily with fennel, typically with some black pepper and occasionally with sweet basil or cayenne pepper flakes (I believe it’s mostly based on Italian luganega, but I’m not certain about that). It’s almost never smoked though, so I’m not sure if it is what these recipes are calling for or not. In theory, Bologna sausage would fit the description of ‘smoked Italian sausage’, and it’s readily available in the US, but that’s probably not it since most Americans don’t even know it’s sausage (we largely just use it as a cold-cut for sandwiches under the name ‘baloney’).  After digging a bit further, I’ve learned that apparently some places in the US that make smoked meats actually smoke American-style Italian sausage and sell the result as ‘Smoked Italian Sausage’, and some people go about making these themselves as well. I’ve never had these myself (let alone seen them sold anywhere), but my guess is that they are what the recipe is calling for when it says ‘Smoked Italian Sausage’. From what I can tell, these sausages are usually hickory-smoked like many other smoked meats in American cuisine that don’t call out a specific wood used for the smoking. 