Difference between Peptone, Peptide and Proteose
Quick Answer


Peptide refers to at least two amino acids joined by amide bonds.
Proteoses are products of acid proteolysis which precipitate with saturating ammonium sulfate.
Peptones are products of acid proteolysis which do not precipitate with saturating ammonium sulfate.
While peptide is a term of significant relevance today, proteose and peptone are anachronistic.




Long, Confusing and Out-Dated Details

The terms peptone and proteose were first used in the late 19th century, which makes finding substantive definitions, well, difficult. I refer you to the following paper (yes, 1891...). It is not the first to discuss proteoses, but I can't find any earlier ones and the explanation is quite clear (emphasis added).

Chittenden RH, Hartwell JA. 1891. The Relative Formation of Proteoses and Peptones in Gastric Digestion. J Physiol 12:12-22.


  In the digestion of proteid matter by pepsin-hydrochloric acid there are three well-defined products or classes of products, viz. acid-albumin or syntonin, albumoses or proteoses, and peptones. We look upon the first as the initial product of gastric digestion and identify it by its well known precipitation by neutralization. In the filtrate, the [proteoses] can be detected... best by saturation with ammonium sulphate, while the true peptones... are found in the filtrate from the latter precipitate... True peptones are bodies not precipitated by saturation with ammonium sulphate, and are the final products of pepsin digestion. 


NB: proteid = protein

So, according to this paper (and apparently "all physiologists" at the time, see below), there are three main products resulting from pepsin-acid digestion of protein:


syntonin - the initial product, precipitates upon neutralization (likely due to acid denaturation)
proteose - the main product after continued digestion, characterized by precipitation with saturating ammonium sulfate


  Study of the individual proteoses formed in the gastric digestion of albumin, fibrin, globulin, myosin, casein and other proteids has seemingly already shown that these so-called preliminary bodies are the main products of the digestive action of pepsin

peptone - the final product of digestion, does not precipitate with saturating ammonium sulfate


  All physiologists are presumably agreed that peptone is the final product of gastric digestion



They further emphasize that peptone is a product of continued proteose digestion:


  Since the discovery of the [proteoses] and of their characteristics, frequent study of digestive mixtures has given convincing proof that in an ordinary gastric digestion of any common proteid only a comparatively small amount of peptone is formed; peptonization in the true sense of the word results only from the long-continued action of pepsin-acid, and even then complete peptonization rarely if ever occurs. The... proteoses are to be considered as the primary products of gastric digestion, while peptones are the end products of proteolytic action, the latter being formed by the gradual hydration of the primary products...


It would seem that peptone differs from proteose only in the length of its constituent peptides, with peptone containing shorter peptides due to continued proteose digestion. However, a more recent paper (with more recent meaning 1924) challenged this view and claimed that both proteose and peptone consist of small peptides which differ in amino acid composition rather than length. In their view, different composition rather than length explains their differential solubility in saturating ammonium sulfate.

Rudd GV. 1924. Proteoses, Peptones, and Polypeptides. Aust J Exp Biol Med Sci 1:187-190.


  ...each fraction must consist of a mixture of comparatively simple peptides, which differ among themselves in the amino-acid units of which they are constituted. The fact that some, at least, of these peptides are precipitated by ammonium sulphate shows that they belong to the group of proteoses, which therefore are partially, if not entirely, made up of simple peptides.
  
  It is possible that the terms, "proteose," "peptone," and "polypeptide,*' will all have to be considered to apply to substances of the nature of peptides... each built up of a small number of amino-acid units and differing from each other, not so much in the number of amino-acids in the molecule, but rather in the variety of these acids. The differences in solubility in various solutions shown by these compounds are thus to be attributed to differences in their chemical constitution, rather than in their molecular complexity. If this be so, these substances would be considered, not as successive stages in hydrolysis, but as products of one completed stage, differing in their solubility's.


They also quote another paper with supporting evidence:


  Fischer produced tripeptides and tetrapeptides of known composition and structure, which were precipitated when their aqueous solutions were saturated with ammonium sulphate. If these peptides were found in the solution obtained by the hydrolysis of a protein with pepsin they would be classed as proteoses.


I wasn't able to find any subsequent research. Nevertheless, such definitions from this period are based on macroscopic physical, rather than molecular, properties of the substance. This old terminology is not particularly informative in modern biology, and it would seem that they remain in use only as historic anachronisms. Today, both peptone and proteose are terms used almost exclusively when describing microbiological culture media (which dates from the period) or when making general reference to digestion products. In fact, they are often used in conjunction (ie proteose-peptone) which suggests they are now synonymous.