The Lat. etymon of this base type does not pose a problem: It is a Greek loan word which is composed of tyrós (ὁ τυ̅ρός) 'cheese' and boūs (ἡ βοῦς: cf. Lat. bovis) 'cow'. The emphasis on cattle-cheese that is expressed by this word formation marks the product as something distinctive and indicates that KÄSE originally was not produced using COW'S MILK. To this day, cheese is customarily produced using sheep's and goat's milk in Greek culture (compare this corresponding depiction from the Polyphemus-episode in the Odyssey [9,170-566; esp. 244-247]; Polyphemus does not own any cattle).
τὸ βούτυ̅ρον is Greek for 'the milk's fat' (τὸ πῖον τοῦ γάλακτος [Corpus Hippocraticum]). The Corpus Hippocraticum (a collection of medicinal texts that were recorded between the sixth century BC and second century AD) gives an account of the Scythians producing cheese from mare’s milk (Corp. Hipp., Morb. 4, 20). The method described therein has remained the same and is occasionally applied to this day. Reportedly, the Scythians filled a barrel (hollow wooden vessels: ἐς ξύλα κοῖλα) with the mare’s milk which was then shaken. It is not specified in the Corpus Hippocraticum what the butter was used for by the Scythians (as a food or as a remedy).
Similar to the Corpus Hippocraticum, the impression of the use butter as something typically 'barbaric' emerges when reading Pliny the Elder (NH 28, 35: e lacte fit et butyrum, barbararum gentium lautissimus cibus et qui divites a plebe discernat). This may be due to the (still) predominant use of olive oil as cooking fat in the Mediterranean world. In the Greco-Roman region, butter seems to have been used more as a remedy rather than a cooking ingredient. There certainly are numerous records of βούτυ̅ρον/butyrum in the context of medical literature (i.a. in Celsus and Galen, apart from Hippocrates). Pliny the Elder also denotes the use of butter as a remedy (e.g., against neck pain: NH 28, 52)
In addition to the neuter gender βούτυ̅ρον, there is also the masculine version ὁ βούτυ̅ρος. In both cases, the accent falls on the third to last syllable (proparoxytone). The Greek word seems to have been adopted into Latin (butyrum).

There are two accent variants of the base type butyru(m) that need to be distinguished:

paroxytone Lat. butӯru(m) which is the origin of the Ita. type butirro (cf. DELI 179);
Lat. bútyru(m) with the accent on the initial syllable which was inherited from Gr. βούτυ̅ρον. From this came the Old French bure resulting in Modern French beurre. This type was borrowed by Italian and led to Ita. burro (cf. DELI 178).

It is not obvious how the word was transferred from Romanic into Germanic. Take note of the varying gender in Ger. Butter: In Alemannic and Bavarian the masculine type is dominant while the SDS also documents instances of the feminine and even one neuter gender. Kluge, 166 views the masculine type as a secondary development analogous to the masculine Alemannic synonym Anke while the feminine version, which he describes as the result of a conversion from neuter plural -a to feminine singular, prevailed. This is in line with Old High German butira. However, considering the interlingual geolinguistics of the Alpine region, this explanation is not convincing. The masculine type in the Bavarian language region of Tyrol shares an area with the equally masculine Roa. type but'ir which borders to the south. It is thus much more probable that this form is the primary substratal loanword while the feminine type die Butter is a secondary variation. Because of the dental -t-, the loanword was likely not formed before the eight century AD, but rather after the second sound shift.
Therefore, it seems that the type butyrum largely repressed the meaning of 'to grease' contained in Lat. unguere / *ungere.