Blues is a language, with grammar and vocabulary. The difference between learning to play the blues and learning to play a blues is the same as the difference between learning to speak a language and learning just some words or phrases in that language.
In the vocabulary instead of words you are using scales and chords. In the grammar instead of order of words you are using harmonies.
The vocabulary in blues includes the scales: minor and major blues, minor and major pentatonic, mixolydian, and dorian. Those are used prominently, but there are many more. Some like to use the lydian b7 mode, for example. The vocabulary also includes the dominant 7 chords, which are very common.
The grammar (harmony) includes the various I7 IV7 V7 progressions (in different orders), like the classic 12 bar blues. The harmony in general tends to be heavily based in dominant 7 chords.
That's a very simplistic overview, and there's much more to it (minor blues, other modes, swing, the list goes on), but hopefully it is enough to give you an idea of what blues is as a language. If you want to learn the language you have to dive into it: teachers, lessons, books, tutorials, listening, transcription, practice, Music SE!, etc.