Is there a difference in the practice of satipatthana bhavana and vipassana bhavana? Or are both terms synonyms?
Vipassanā is the same as satipatthana bhavana. Essentially the practice is from Satipatthana Sutta and/or Anapanasati Sutta or similar Suttas are called Vipassanā as they help to see clearly the true nature of phenomena.
Yes there is a difference, and no the terms are not synonyms.
Sati-patthana bhavana is the setting up of mind or memory, vipassana bhavana is the setting up of the insights on which that setting up of mind or memory is based.
You do not say that purchasing the ingrediants for a loaf of bread is the same thing as the use of those ingrediants in the making of the dough.
It is a common error to mistake sati for satipatthana and for vipassana practice to be identified as limited to the satipatthana sutta (or a tiny fraction of it as in teaching people how to breath for the big bucks).
Satipatthana is not the same practice as Anapanasati. They have two entirely different aims. The Satipatthana is aimed at setting up the mind: "Thus he sets up memory just sufficiently to gain a measure of knowledge, a measure of recollectedness."
Anapanasati is aimed at setting up the method for liberation: "On thelook-out for opportunities to let go, I will inspire, this is the way he trains, On the look-out for opportunities to let go, I will expire," this is the way he trains.
That the two practices utilize the same elements and merge does not make them the same things.
Various translations of the Satipatthana sutta: http://buddhadust.net/backmatter/indexes/sutta/dn/idx_digha_nikaya.htm#p22 .
Various translations of the Anapana samyutta: http://buddhadust.net/backmatter/indexes/sutta/sn/05_mv/idx_54_anapanasamyutta.htm
There is no such thing as "vipassana bhavana" since "vipassana" ("clear seeing"; direct insight) is not something that can be practised or "developed" ("bhavana") via an act of will (refer to AN 11.2).
MN 149 says satipaṭṭhānā is developed (bhāvanā) and vipassanā occurs (vattanti):
When he develops (bhāvayato) this Noble Eightfold Path (ariyaṃ aṭṭhaṅgikaṃ maggaṃ), the four foundations of mindfulness (satipaṭṭhānā) also come to fulfilment (pāripūriṃ) in him by development (bhāvanā); the four right kinds of striving also come to fulfilment in him by development; the four bases for spiritual power also come to fulfilment in him by development; the five faculties also come to fulfilment in him by development; the five powers also come to fulfilment in him by development; the seven enlightenment factors also come to fulfilment in him by development. These two things — serenity (samatho) and insight (vipassanā) — occur (vattanti) in him yoked evenly together.
Therefore, satipatthana bhavana and vipassana bhavana are not synonyms, even though vipassana is a fruit/result of satipatthana.