Tl;dr

old handle + new heads: fine

new handle + old heads: incompatible

Are Jordan Clinic Easy Clean Flosser and Jordan Miracle compatible?

Jordan Clinic Easy Clean Flosser floss heads are backward compatible with Jordan Miracle handles, but Jordan Miracle floss heads are not compatible with Jordan Clinic Easy Clean Flosser handles.

The Jordan Clinic Easy Clean Flosser handle is not backward compatible with Jordan Miracle floss heads, but the Jordan Miracle handle is compatible with Jordan Clinic Easy Clean Flosser floss heads.

Are they compatible?
Easy Clean handle Miracle handle
Miracle floss head no yes
Easy Clean floss head yes yes
Can I buy and use Jordan Clinic Easy Clean Flosser floss heads with my old Jordan Miracle handle?

Yes.

The newer Jordan Clinic Easy Clean Flosser floss heads can be attached to an old Jordan Miracle handle.

Can I use my old Jordan Miracle floss heads with my new Jordan Clinic Easy Clean Flosser handle?

No.

The old Jordan Miracle floss heads have two additional ridges in the attaching part compared to the newer Jordan Clinic Easy Clean Flosser floss heads. Whereas the old Jordan Miracle handle has the matching two grooves to fit the extra ridges, the Jordan Clinic Easy Clean Flosser handle does not have those grooves.

Jordan Miracle floss head Socket end of Jordan Miracle handle
A Jordan Miracle floss head and the socket end of a Jordan Miracle handle. Note the extra ridges on the floss head and the matching grooves on the socket.
Jordan Clinic Easy Clean Flosser floss head Socket end of Jordan Clinic Easy Clean Flosser handle
A Jordan Clinic Easy Clean Flosser floss head and the socket end of a Jordan Clinic Easy Clean Flosser handle. Only the center ridges and matching grooves are present. (The outer oval-shaped extra bit, with matching cutout in the socket, is beyond the height of a Miracle floss head and does not interfere with compatibility.)
I have a Jordan Miracle handle, which floss heads should I buy?

You can buy either Jordan Miracle or Jordan Clinic Easy Clean Flosser floss heads, as both will work.

If both types are available, the Jordan Miracle ones may attach slightly more firmly (due to matching connectors), but if you lose or break your old Jordan Miracle handle, and replace it with an Easy Floss handle, the Jordan Miracle floss heads you've bought will not be compatible with the new handle.

Jordan Clinic Easy Clean Flosser floss heads will work with your old handle, and they will also be compatible, should you replace your old Jordan Miracle handle with a new Jordan Clinic Easy Clean Flosser handle at some point.

Jordan Miracle floss heads do not have added fluoride, whereas Jordan Clinic Easy Clean Flosser floss heads do have added fluoride.

I have a Jordan Clinic Easy Clean Flosser handle, which floss heads should I buy?

You should buy Jordan Clinic Easy Clean Flosser floss heads; Jordan Miracle floss heads are not compatible with your handle.

I have Jordan Miracle floss heads but no handle, which handle should I buy?

You should buy a Jordan Miracle handle to utilize Jordan Miracle floss heads, as Jordan Miracle floss heads are incompatible with the Jordan Clinic Easy Clean Flosser handle.

I have Jordan Clinic Easy Clean Flosser floss heads but no handle, which handle should I buy?

If both types are available, I recommend that you buy the Jordan Clinic Easy Clean Flosser handle.

Both the Jordan Miracle and the Jordan Clinic Easy Clean Flosser handle will work with your Jordan Clinic Easy Clean Flosser floss heads. However, as the handles usually come with some refill heads in the packaging, you will receive Jordan Miracle floss heads with a Jordan Miracle handle, and those will be incompatible with a Jordan Clinic Easy Clean Flosser handle, should you replace the Jordan Miracle handle with a new Jordan Clinic Easy Clean Flosser handle at some point.