This simile, of course, derives from the fact that two peas from the same pod are virtually indistinguishable. The phrase, which is sometimes given as 'like as two peas', is quite old and versions of it date from the the 16th century. For example, John Lyly used the phrase in Euphues and his England, 1580:
"Wherin I am not unlike unto the unskilfull Painter, who having drawen the Twinnes of Hippocrates, (who wer as lyke as one pease is to an other)."
Lyly's use of 'pease' as the singular form was the norm in Tudor England. The word 'pea' came into use as the singular in the 17th century, with 'peas' as the plural. This avoided 'peases', which would have been somewhat of a mouthful. That transition left 'pease' out in the cold and we now hardly use that form, except in the name of the dish of dried peas, cooked to a mush - 'pease pudding'. The pudding is itself now becoming less common as it has been largely superseded by 'mushy peas', which is essentially the same thing. Once that process is complete, 'pease' will be gone from the everyday language - a pity.