I beieve the plant in your hand hand in the second pic may be a burros tail. Not exactly sure how to root a cutting of it but i think all succulents root fairly easily, if slowly, in just regular potting soil as long as things dont get too moist.
Not sure about the other plant.
Im sure plenty of others will chime in with lots of info.

Newbi, the second (almost) resembles a Burro's Tail, or in the same family..My BT has rounder leaeves.
Pirate Girl is good at ID'ing succulents so she can help you, WHERE ARE YOU KAREN?

Both succulents can be propagated by setting leaves atop soil..Actually the first plant (stem/branch) needs to be planted in soil, whereas the second will root when leaf is set on top of soil..I do this w/my BT when leaves rub against something and fall..they root rather easy..Toni

I'll just pop in and say, AWESOME PLANT! Very well grown.

Susan

Definitely the sedum 'burro's tail'...Sedum morganianum. The one with more 'rounded' leaves is the cultivar called S. morganianum 'burrito', Toni.

The other is likely a sedum, too, or a sedeveria....hard to tell without blooms....(and often hard to tell *with* blooms, LOL!) check out this website with great sedum photos.

Repotting these is so tricky, because they're so brittle. I potted mine into a larger pot once and lost a *whole* lot of leaves! I have since just left it alone and never move it.

Here is a link that might be useful: Sedum photos

Thanks Nan...I know what you mean about repotting..I planted in a ceramic donkey planter, about oh 5-6 yrs ago and it's still growing in the same pot..LOL..No drainage, but it's fine. Toni

Hi SusanCarol, long time no see - HOWDYYYY!

Thx Toni, I appreciate the vote of confidence.

Unfortunately, I'm not sure abt Newbie's 1st plant, am guessing it's some Grapto somthing, Pachyveria or Pachyphytum w/ something else. Nicely grown indeed! To propagate that I'd cut a stem w/ 3 or 4 nodes on it, remove the bottom set of leaves, leave it out for a couple of days to harden & than plant it in DRY C&S mix, w/ or w/out rooting hormone & DO NOT WATER IT IN. That's how I'd handle the broken off piece too, I'd suggest you could place it back in mother plant's pot, or you could give it a small pot of its very own.

As to repotting the whole plant, not sure why, were you going bigger or refreshing the soil? I'm not sure it wants bigger, one can just take it out carefully, refresh the soil w/ more of the same if you wish & then removing any dry, brittle or broken off roots, place it back in the pot.

The other is Sedum morganianum (BT) looks happy, I just place the leaves on top of the mix (as Toni suggests) & leave it DRY until one sees new growth.

Nice work, enjoy!

Thanks everyone! Wow... you're all very knowledgeable. I googled some images of the various names you've suggested. One does appear to be Sedum morganianum (Burro's Tail), I took a look at the web-page that was suggested and am wondering if the other plant is Sedum adolphii. What do you think?

I will do as pirate girl suggested with planting and not watering (although for how long do I withhold all water?). Also, what can I do to encourage the plant to return to normal colour and get rid of the pale sickly green (I presume from the overwatering that happened awhile ago)?

Thanks everyone!