Bosnian, Serbian and Montenegrin are separate standard languages quite similar to the Standard Croatian (some people consider them 'variants' of a single language). I will summarize the most important differences.
The major difference is that Serbian and Montenegrin use another alphabet — Cyrillic. However, each letter of Croatian Latin corresponds to one letter of Serbian Cyrillic.
Actually, today in Serbia the Cyrillic alphabet is mostly used in official and ceremonial uses. Majority of newspapers are published in 'Serbian Latin' (identical to 'Croatian Latin') script. Web sites published in Cyrillic have usually a 'LAT' button somewhere. For instance, Politika daily has pages both in Cyrillic and Latin (check CYR and LAT links on top), but B92 TV is in Latin only. Even the web site of Serbian government has links ћирилица Cyrillic and latinica Latin on the top (Cyrillic is chosen by default). Statistics show that about 1/6 of text on Serbian web sites is written in the Cyrillic script.
Besides using Cyrillic script sometimes, there are few differences in spelling (both in Serbian Latin and Cyrillic). The first one is spelling of foreign names. Serbian and Montenegrin usually respell them using approximated pronunciation:
|George Bush||Džordž Buš||Џорџ Буш|
The second difference is spelling of the future tense. When an infinitive in -t is immediately followed by an auxiliary ću², ćeš²... it's spelled together, and the infinitive-final -t is discarded, with possible sound mutations:
|reći ću||reći ću||рећи ћу|
People usually associate Ekavian (mleko, pesma) and not Ijekavian (mlijeko, pjesma) — with Serbian, but it's not really true, since Serbs use both as standard: most Serbs outside of Serbia (e.g. Bosnia, Croatia and Montenegro) use Ijekavian, and Serbs in most of Serbia, including Belgrade, use only Ekavian. You can find both in Serbian newspapers. The Serbian Standard is much less strict than Croatian, there is a bigger choice of "acceptable" variants.
If you find a 'dictionary of differences' listing bijeli as 'Croatian' vs. beli as 'Serbian' you can immediately conclude it's oversimplifying things (and listing completely predictable differences!).
Serbian has some specific nouns:
|čas||sat||lecture, class in school|
|lenjir||ravnalo||rule (to draw lines)|
|sprat||kat||floor (of a building)|
|točak (točk-)||kotač||wheel (not to steer)|
|bezbjedan (bezbjedn-)||siguran (sigurn-)||adj. secure, safe|
Here Serbian words are given in Ijekavian forms, it's trivial to obtain Ekavian forms that are normally used in Serbia.
Especially, terms related to cooking, food, and standard house items show numerous differences; these terms are often completely unknown outside their 'territory':
|boranija||mahune f pl.||green beans|
|makaze f pl.||škare f pl.||scissors|
There are several specific verbs as well:
ćutati (ćuti) be silent (Cro. šutjeti/šutiti)
pomjerati («) ~ pomjeriti move, shift (Cro. pomicati (pomiče) ~ pomaknuti (pomakne)
There are numerous differences in scientific terms, especially chemistry and biology:
|cell (in biology)||stanica||ćelija|
However, prison cell is just ćelija in both Croatian and Serbian. Croatian uses obitelj f for human family, while Serbian uses porodica, and both usually use just porodica for families in biology (sets of closely related species).
There are also different terms in math:
|straight line||pravac (pravc-)||prava|
Some words have only a slightly different form due to different adaptation of foreign words (this table includes only characteristic words showing ways words differ):
Some words adapted from Greek have k- in Croatian, and h- in Serbian:
Two more verbs are used a bit differently in Serbian.
The verb smjeti (smije, smio, smjela) may – in Ekavian form smeti – has an additional meaning in Serbia: dare.
The verb umjeti (umije, umio, umjela) know how – in Ekavian form umeti – is quite common in Serbia:
Umijem da plivam! I know how to swim. (Ijekavian)
Umem da plivam! (the same, Ekavian)
Bosnia-Herzegovina is today officially tri-lingual, as evidenced by this warning on a box of cigarettes that displays three identical sentences (the first one is just in Cyrillic; I have taken a photo of an actual box):