The second one is Mazus miquelii (Creeping Mazus).

The first is Laurentia fluvatilis, aka blue or white star creeper. The second is what is sold here as Mazus reptans.

Both need moist soils and/or routine watering so perhaps not the best choices for a hot, dry location.

Hi, thanks, these would be in hot sun, but not dry. They would be watered. I am trying to cover this ground with some type of creeping groundcover. If these wouldn't work, I was wondering about some type sedum or these sedum tiles I have seen on the web and at HD. Carol

Sedums will work but not exactly stepable - they crush when walked on :-) Have you considered a creeping thyme? Or dymondia?

Thanks, I saw a photo with dymondia and loved it. I ordered and the seller just sent me small plugs. There are only 3 left out of 5. They also haven't moved or grown in around a month. I understand it is slow growing.

I took the pot that was labeled creeping thyme back to the nursery today that sells stepables. They haven't gotten this years inventory, but will in 3 weeks. I had come to the conclusion that it was thyme like elfin thyme, but one of the workers said to smell it. The plant has no smell thus she says it isn't thyme. Right now I am going to wait until their inventory comes in. I believe this - whatever it is - might work. It is small and definitely looks spreadable.

I did look up the specs on the other plant Mazus blue and white. Most said it was hard to keep under control.

This has been an education - Thanks for all your help. Carol

Apart from the tell-tale scent, thyme leaves have the coarse, leathery texture of many Mediterranean type plants which are evolved to reduce transpiration in dry conditions. Your top plant has soft juicy foliage which shows it has evolved under conditions of ample moisture. You can tell a lot about a plant's preferred growing conditions from its foliage.

As stated previously, the 'thyme' is really blue star creeper. And as long as you can provide the consistent soil moisture it prefers, it could work.