Country blues is a broad term but it is mostly used when talking about the earliest form of blues, which took root in the late 19th century in the American South. It is also known as "old-time blues," "acoustic blues," "deep blues" and "traditional blues." This form of blues is always acoustic-guitar driven, and is typically nothing more than a player and his guitar---although early piano-based blues may fall under this category as well.
Delta blues, named after the Mississippi delta from where it originates, is next to country blues as the oldest blues genre. They have much in common. Both are acoustically driven, guitar-focused genres. But while country blues focused on finger-picking "rural" guitar sounds, delta blues turned the focus to slide guitar, creating a more passionate, powerful sound that was at the time exclusive to the blues. Many of the earliest blues recordings from the 1920s are delta blues recordings.
While most blues is known for being downbeat and slow, jump blues is up-tempo and energetic. A combination of swing, blues and jazz, it was commonly played by large orchestras or bands with horns sections. It became popular in the mid to late 1940s and is seen by some as the precursor to rock and roll thanks to its upbeat style, even though it usually relegated the electric guitar to the rhythm section.
When blues musicians moved north in the 1940s, they took the blues sound with them. What was originally a musical genre for a lone player and his guitar quickly changed in the clubs of the city, with harmonica players, horn sections and drums joining the line-up. This full-featured band version of the blues helped to influence nearly every genre of blues that came after it and helped lay the groundwork for what became rock music in the 1950s.
Modern blues-rock came out of England in the 1960s, when artists like Steve Winwood and Eric Clapton took their love of classic blues and combined it with the pop-rock sound of acts like The Beatles. Blues-rock places heavy emphasis on guitar riffs, and its guitar-centric sound helped influence 70s rock and eventually helped to create heavy metal.