Difference between therapy mode and modality?

You see that you found "modality" being the state or quality of being "modal", and then when looking up "modal" you find that it means "of or relating to modality." This is quite circular and unhelpful.

The Merriam-Webster definition that comes closest to the modality that you're talking of is:

4 : a usually physical therapeutic agency

Therapeutic agency. I must say Merriam-Webster isn't as clear about this as it could be. So let's look at a definition from the American Heritage Dictionary:

5. Medicine A therapeutic method or agent, such as surgery, chemotherapy, or electrotherapy, that involves the physical treatment of a disorder.

This is a lot clearer, and sounds a lot like a mode of treatment. It is often used in medicine, but it also has a general use, albeit in formal, academic or field-specific contexts. Here is a more general definition from Oxford Living Dictionaries:

2A particular mode in which something exists or is experienced or expressed.
Oxford English Dictionaries

When people refer to treatments, whether medical or psychotherapeutic, as modalities, they mean mode/method/procedure, as in different types of treatment. Why say "modality" instead of mode? Well often there are alternative/alternate ways of saying things. Someone might say:

"The total of the expenses is..."
or
"The totality of the expenses is..."

The language may change depending on what specialist field you are in.

As far as my claim goes that "modality" can in many instances mean simply "mode", I refer to the Wikipedia disambiguation page for "modality"
Modality disambiguation page

You can see that in the fields of science and technology "modality of transport" simply means "mode of transport", in other words whether you take a car or a train.

In medical imaging "imaging modality" simply means the mode/technology of imaging used, ie., X-ray or MRI.

A "diagnostic modality" is a mode/method of diagnosing, ie., examining medical history, physical examination and other tests.

So yes, in many cases "modality" is just a longer word for "mode" (not always).

Coming to your example of therapy, you'll see the entry:

Modality (therapy), a method of therapeutic approach

So there you are, mode, method, modality, they sound very similar to me.

In fact, I think it makes my point that if you click on any of these "modality" examples I've given it doesn't bring you to an article named "modality of", but simply something like "mode", "method", "type", or "procedure" as sub-headings of their respective articles.

• "modality of transport" brings you to the "mode of transport" article.
  Mode of transport
• "Modality(medical diagnosis)" brings you to the "Procedure" section of the "Medical Diagnosis" article.
  Medical diagnosis: Procedure
• "Modality(medical imaging)" brings you to a non-existent article, but presumably should redirect simply to "Medical imaging" under the "Imaging modalities" sub-heading that lists the types of imaging.
  Medical Imaging
• "Modality(therapy)" brings you to the "Therapy" article under the sub-heading of "Types of therapy".
  Therapy: Types of therapy