Your plant appears to be Crassula ovata, commonly known as Jade plant. also money plant, but the latter name is confusing, since it's used for other plants too. Yours looks nothing like it should do - it should have leaves all over the stems (image of a small one here https://www.amazon.com/Sunset-Jade-Plant-Crassula-House/dp/B0044FQDRG) If a leaf drops to the soil, it often roots itself, as you describe.
I've been hesitating to answer this, because my inclination would be to cut this poor thing right back almost to the main trunk, leaving 4 nubs or bits of stem coming off it. This is a bit risky, but I'd still do it anyway - its the right time of year to chance it, but the plant may not respond, although I can see some smaller shoots near where I'm suggesting cutting back to, which is hopeful. Do not cut back past those little shoots, just above them will be fine.
It needs a larger pot - turn it out of its pot and see how tightly packed the roots are; I suspect they're very tightly packed indeed, so if that's the case, use a pot that's big enough to give an inch or so of space all round and beneath in the new container. Use new potting soil, adding a good helping of perlite or vermiculite to improve drainage, maybe a little horticultural grit if you can find any, mixing all together prior to repotting. The pot should have drainage holes, and when you water, empty out any outer pot or tray after 30 minutes, so it is not left sitting in water.
These plants often develop a red rim round the leaves with lots of sun exposure - the leaves going entirely red can mean the leaves are about to turn brown and drop off, so it may be yours is getting a little too much sun exposure, or it's just that it can't cope because its roots are so cramped. Further information here http://sosplantcare.com/jade-plant-care/
In regard to the second, younger plant, I see no new growth low down... I suggest you try the above treatment on the larger one, and if that reacts positively and starts producing new growth, then risk doing the same with the second one. It might also be wise to remove one or two of the leaves from the larger plant and pop them on top of the soil to see if they root...that way, you'll have replacement plants if necessary!
