A phone is a class of sounds (as opposed to their instances which are all unique) that can be reliably described by articulatory or acoustic features (phonetics) or by patterns found in EEG (I'm thinking of MIT's voiceless mic).
A phoneme is another type of "sound" class used in linguistics and it is arguably the more important: phonemes, as studied in the context of a particular language, is the finite set of sounds (a few dozens at most) from which you build different words in that language. Phonemes always come in pairs, since they are defined as the minimal distinctive linguistic unit that can yield a difference in meaning.
Substitute /p/ with /f/ in/fear/ and you get /pear/, i.e. another word, a difference in meaning --> thus /p/ and /f/ are phonemes.
But substitute /r/ with /rrrrr/ in /Braveheart/ and you get the same word but with a scottish accent. These do not form a phonemic pair but allophonic variations of the same phoneme (here according to different geographic areas but they can also vary according to age, social status, gender, etc ...)
https://en.wikipedia.org/wiki/Vowel_length#Contrastive_vowel...
It's one of the most difficult things to pick up when learning Japanese as well. There are lots of words that are basically homophones except for vowel length and tone. To an English speaker they tend to sound identical, but to a Japanese speaker if you get it wrong the result is unintelligible. For example "地図" (in romaji: chizu and pronounce cheezu with a short "ee") is "map" and "チーズ" (in romaji: chiizu and pronounced cheezu with a long "ee") is "cheese" (though they have the same tones... I'm struggling to think of an example with different tones as well as vowel length).
The thing that helped me the most for this was singing songs. Once you understand that there is a necessary rhythm to the words, it makes it much easier to use that rhythm in speaking. Or at least it did for me -- YMMV.
Itabashi Station: https://en.wikipedia.org/wiki/Itabashi_Station
Iidabashi_Station https://en.wikipedia.org/wiki/Iidabashi_Station
(the major difference you hear is the long ii, rather than the t/d difference)