Question 1 - in basic 101 for student like moi:
What's the difference and/or relations between Dracaena and Cordyline ?
I salvaged from a nursery what we call here in Israel Red Dracaena australis, and which is called in several sites - Red Cordyline - hence the above confusion - in Question 1.
The tall trunk (about 5 feet tall) is damaged - the "tip", the "heart" broke !
From the base there is a new healthy baby stem growing. - see in first picture
Question 2 - If i will cut the trunk just under the crown - see in second picture (at finger point) - will it yield/grow a split of trunks at the top (just under the cut) ? (the way Dracaena tricolor or red margins Draceena do) !
WILL IT SPLIT ? and Dracaena / Cordyline ?
I'm just going on instinct here, but I would cut it at the base where the new growth is. You can also scrape the bark of the dead-looking stem with a fingernail to see if there is anything green (living) underneath. Do this at various points until you hit living tissue and cut below that. This works for most other plants, but I am not an expert. This is how I determine how far to cut back my tropicals that have sustained a little frost damage. In any case, you must determine where the living tissue is.
I believe LadibugZ9 is right. I vote yes to this....
I agree too, chances are the plant may be dead right underneath where the leaves are, you will probably have to cut farther down the trunk to find the live part.
And to answer your first question about Dracaena and Cordyline--they are VERY closely related to each other, there are some plants that have gone by both names at one point or another, if you look in Plant Files you will see there are some plants listed as Cordyline that have a synonym of Dracaena and vice versa. From a botanical standpoint there must be a difference between them, but since they are so closely related and there's been confusion in the naming, to the eye of the average gardener I doubt you'll be able to find one or two key characteristics that will tell you for sure which one it is. The best thing to do if you're in doubt is post a picture in the Plant Identification forum, chances are someone there will recognize what you have.
Aren't Cordilines the same as "Ti" plants? The ones you get a little "log" of and then lay it down in water and it grows into a nice plant?
IF they are, then Ronnie could cut the stem in several pieces (the live parts), seal the ends with wax or something and grow a new plant from these sections. I am NOT 100% sure on this. I know someone else will jump in and correct me.