It IS kind of confusing, isn't it? I'll take a stab at clearing the muddy waters for you.

The plant that you are calling 'ribbon plant' is Dracaena sanderiana. It is often (maybe even mostly) the plant used in the 'Lucky Bamboo' style. The other plant that you have pictured is (what appears to be) a different cultivar of Dracaena sanderiana, commonly called Belgian Evergreen. It, too, is very often used in 'Lucky Bamboo' trained plants.

There are probably other cultivars of Dracaena sanderiana out there, as well. I sure wouldn't be surprised!

Cane plants can be induced to sprout at the nodes via pruning, air layering, stem cuttings, etc. That is why the Belgian Evergreens are sending out side shoots. Their axillary growing point has been removed, unlike the 'Ribbon Plant' in your first image.

Here is a link that might be useful: Belgian Evergreen

You have discovered the confusing world of common names. The same plant can have different common names, to be sure of what you have you need the latin name. Latin names have a genus and a species name, the genus name refers to a group of closely related species, the species name refers to a specific plant. To use dogs as an example, the household pet is Canis canis, the wolf is Canis lupus, both are Canis.

Then, to add to confusion, the same plant can have different varieties. Think of dogs, you can own a poodle or a Mexican hairless or a German Shepard but they are all dogs and all the same species Canis canis.

Lucky Bamboo is one type of dracena sanderiana as is ribbon plant. As Lucky Bamboo is more a marketing term than a specific plant, if you look around you can likely find Lucky Bamboo in water that looks just like your ribbon plant and find plants growing in soil and labelled Dracena that look just like your Lucky Bamboo. Neither is true Bamboo which is a grass. For a discussion, see the link below. Part way down the page there is a link to a picture of true bamboo.

Here is a link that might be useful: Dracena and Bamboo

Thank you both. :3