The Hobbits were certainly related to the Rohirrim, as their languages share a lot of similarities. The word "hobbit" seems to have originated thus:(Appendix F)
Hobbit was the Name usually applied by the Shire-folk to all their kind. Men called them Halflings and the Elves Periannath. The origin of the word hobbit was by most forgotten. It seems, however, to have been at first a name given to the Harfoots by the Fallowhides and Stoors, and to be a worn-down form of a word preserved more fully in Rohan: holbytla 'hole-builder'.
lotr.wikia.com has a very good description of their history, which I will shamelessly copy and paste here:
Historically, the Hobbits are known to have originated in the Valley of Anduin, between Mirkwood and the Misty Mountains. According to The Lord of the Rings, they have lost the genealogical details of how they are related to the Big People. At this time, there were three breeds or tribes of Hobbits, with different physical characteristics and temperaments: Harfoots, Stoors and Fallohides. While situated in the valley of the Anduin River, the Hobbits lived close by the Éothéod, the ancestors of the Rohirrim, and this led to some contact between the two. As a result, many old words and names in "Hobbitish" are derivatives of words in Rohirric. About the year TA 1050, they undertook the arduous task of crossing the Misty Mountains. Reasons for this trek are unknown, but they possibly had to do with Sauron's growing power in nearby Greenwood, which was later named Mirkwood because of the shadow that fell on it as Sauron searched the area for the One Ring. The Hobbits took different routes in their journey westward, but as they began to settle together in Bree-land, Dunland, and the Angle formed by the rivers Mitheithel (Hoarwell) and Bruinen (Loudwater), the divisions between the Hobbit-kinds began to blur.
They probably just changed from the rest, like the Druedain.
Also, here are some quotes from The Letters of JRR Tolkien:
Letter 131:
In the middle of this Age [the Third Age] the Hobbits appear. Their origin is unknown (even to themselves)† for they escaped the notice of the great, or the civilised people with records, and kept none themselves, save vague oral traditions, until they had migrated from the borders of Mirkwood, fleeing from the Shadow, and wandered westward, coming into contact with the last remnants of the Kingdom of Arnor.
† The Hobbits are, of course, really meant to be a branch of the specifically human race (not elves or dwarves) . . .
That confirms that the hobbits are essentially human, just a different (shrunken) variety.
