Like vehicle gearboxes- there are 'Automatic' and 'Manual'
Smart Collections are 'automatic' they continually search for images based on the criteria defined in the Smart Collection dialog window. LR installs with a couple of SCs as examples. You can design your own to suit your needs. They work like a filter, always showing images that meet the criteria. eg. 5-star rated *****
Standard Collections are 'manual', they contain nothing until you add images to the collection. They are most useful to gather images for a specific purpose- Design a Book, Make a slide-show, Send to Grandma, etc.
You can make a standard collection the "Target Collection", then any time you have one or more images selected in the library grid, press [B] to add to the 'Target' collection. (Set Target Collection by a Right-Click of the mouse)
Smart Collections are, well smart, the others are rather dumb
SC’s use actual data to build the collections. Say you want to find all images that are Virtual Copies. Each VC has data that defines them as such and based on using criteria, a smart collection can find them automatically for you. As you build more VC’s, the smart collection will grow. Dumb collections are kind of like a folder you make and drag images into manually. You’re doing the work, nothing automatically updates (they are as I suggest, kind of dumb). Smart Collections are very powerful. Say you want to build a collection that has NO keywords so you can go there and add keywords because that’s important to you. You could build a SC where the criteria is, No Keywords. You’d find all those images and further, as you add keywords, they would automatically remove themselves from that collection. That’s smart!