These apparently similar terms are typically used differently, line breeding being less well defined than linebreeding.
LINE BREEDING commonly involves the creation of a population of similar or virtually identical plants which is referred to as a "line". These plants may have been selected for common desired characteristics (such as a purple line or a tall, spidery purple line). A "line" may be inbred (closed), partially closed, or created with minimal inbreeding.
LINEBREEDING, all one word, is a well-defined term used in animal breeding for the crossing of parents which both trace back in their pedigrees to a specific named ancestor. For an individual to be described as linebred it must be possible to name the ancestor to which it has been linebred.