Wikipedia defines motif quite aptly: Motif is a short musical idea a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition.
What is the specific difference between a motif and a theme, musically?
People generally call "major" themes that represent a major character or place or idea and maybe get their own concert arrangement a "theme", while "minor" themes that might not get played as often or not get a full development "motifs"
For a theme it says: A theme may be perceivable as a complete musical expression in itself, separate from the work in which it is found (Drabkin 2001). In contrast to an idea or motif, a theme is usually a complete phrase or period (Dunsby 2002). The Encyclopédie Fasquelle defines a theme as "Any element, motif, or small musical piece that has given rise to some variation becomes thereby a theme." (Michel 1958–61).
So there are different theories or ideas how each is defined, but apparently nothing truly definitive.
I think that was helpful. Judging by what you posted, could it be said that a theme has more of a self-sufficiency, being able to stand alone outside the work(as mentioned, being able to have a concert arrangement?), that motifs lack. In addition, it has a certain amount of variation, found within the score, allowing the theme to develop. Could it be said that a recurring phrase without development is more of a motif than a theme?