The difference between Modal and Mode

When used as nouns, modal means a modal proposition, whereas mode means one of several ancient greek scales.

Modal is also adjective with the meaning: of, or relating to a mode or modus.

check bellow for the other definitions of Modal and Mode

Modal as an adjective:

of, or relating to a mode or modus
Modal as an adjective (grammar):

of, relating to, or describing the mood of a clause
Modal as an adjective (music):

of, relating to, or composed in the musical modi by which an octave is divided, associated with emotional moods in Ancient — and in medieval ecclesiastical music
Modal as an adjective (logic):

of, or relating to the modality between propositions
Modal as an adjective (statistics):

relating to the statistical mode.
Modal as an adjective (computing):

Having separate modes in which user input has different effects.
Modal as an adjective (GUI):

Requiring immediate user interaction and thus presented so that it cannot be closed until a decision is made.

Examples:

"a modal dialog; a modal window"
Modal as an adjective (metaphysics):

Relating to the form of a thing rather to any of its attributes

Modal as a noun (logic):

A modal proposition
Modal as a noun (linguistics):

A modal form, notably a modal auxiliary.
Modal as a noun (grammar):

modal verb
Modal as a noun (GUI):

A modal window, one that cannot be closed until a decision is made.

Mode as a noun (music):

One of several ancient Greek scales.
Mode as a noun (music):

One of several common scales in modern Western music, one of which corresponds to the modern major scale and one to the natural minor scale.
Mode as a noun:

A particular means of accomplishing something.

Examples:

"What was the mode of entry?"
Mode as a noun (statistics):

The most frequently occurring value in a distribution
Mode as a noun (mathematics, physics):

A state of a system that is represented by an eigenfunction of that system.
Mode as a noun (computing):

One of various related sets of rules for processing data.

Examples:

"In insert mode, characters typed are directly inserted into the buffer"
Mode as a noun (grammar):

A verb form that depends on how its containing clause relates to the speaker's or writer's wish, intent, or assertion about reality.
Mode as a noun (philosophy):

That which exists only as a quality of substance.
Mode as a noun (textiles):

In lace-making, a small decorative piece inserted into a pattern.
Mode as a noun (textiles):

The openwork between the solid parts of a pattern.
Mode as a noun (obsolete):

A woman's mantle with a hood.