They have almost the same surface syntax (with tiny differences), and have very similar implementations (collection of vectors). One could argue that the pre-Hadleyverse R semantics of dataframes is different from Julia’s DataFrames.jl, since the latter is modeled after the “tidy” transformations, but that is almost irrelevant since everyone uses the latter these days even in R (you rarely see the built-in transformations like rbind outside old stats textbooks from the 1990s).
The current incarnation of DataFrames.jl is probably the least surprising part of the Julia ecosystem for an R user. Which is understandable, as it was designed that way. R/Hadleyverse is a great model to copy.