Tent caterpillars that are striped yellow and black? It doesn't sound like tent caterpillars. But presumably you've looked at photos. To answer the other part of your question, no they aren't all related. At least not any more than all birds are the same. Various caterpillars favor different foods and have different degrees of "pest-ness", and plenty turn into wonderful butterflies and moths. Your cottony coccons could maybe be the work of the cabbage moth, especially if the corn is handy to the brassicas. Or it could be one of the untold hundreds of small moths and butterflies that go unidentified by most since they don't get up to anything bad in the garden.

I love your Polka!! It's a climber isn't it? Is that a raspberry near the nest or is it some sort of forsythia berry? I don't know anything about forsythia LOL. Carol

Ok, apparently that white thing's a tailor bird nest. Still don't know whats destroying the leaves though.

Sounds like an infestation of bagworms. Those aren't cocoons at all, but serve as mobile (when young) homes, and later, egg sacks. The females (inside those bags) don't turn into moths at all. A bad infestation can seriously effect the host plant, as you can observe from your spruce. It's too late in the season to do anything about it, other than spend some time removing and destroying each of the bags. You'll be removing the females (if they are still there) or a bag full of next season's eggs. By the way, the caterpillars hatched out early in the spring, as tiny little things. They begin to feed on the host plant (the spruce, in your case) and as they grow, begin to glue bits and pieces of that host plant together to form the bag.