Is a b-movie the same as an independent film?

No.  The first term refers to the production scale and intended market, the second refers to who produced it.

The term "B-movie" dates back to the days from the early to mid 20th Century when going to the movies was an "event" covering several hours.  Besides the "main" feature, audiences watched previews, "shorts" (often cartoons), a "newsreel" segment" and a second picture known as the "B-movie".  B-movies were usually projects shot on small budgets with lesser known talent (thus, the term B-list celebrity still in use today).

Even after theaters shifted away from multiple-film showings, the term "B-movie" continued to be applied to low-budget movies made largely for commercial success rather than artistic merit.

The term "Independent Film" once meant a film produced by a smaller studio outside the "Big Five" Hollywood Studio Establishment (Warner Bros., Paramount, Colombia, Universal and Disney).  The name is a bit misleading today as billion dollar studios like Fox's "Searchlight" and Comcast's "Focus Films" are considered "independents."

no- it means it is made very Cheap and in the Old days theaters ran 2 movies as a set

A B movie or B film is a low-budget commercial motion picture that is not an arthouse film. In its original usage, during the Golden Age of Hollywood, the term more precisely identified films intended for distribution as the less-publicized bottom half of a double feature.

 However, the U.S. production of movies intended as second features largely ceased by the end of the 1950s. With the emergence of commercial television at that time, film studio B- movie production departments changed into television film production divisions making much of the same type of content in low budget movies and series. 

The term B movie continues to be used in its broader sense to this day. In its post-Golden Age usage, there is ambiguity on both sides of the definition: on the one hand, the primary interest of many inexpensive exploitation films is prurient; on the other, many B movies display a high degree of craft and aesthetic ingenuity.