Rambam (Mamrim 2:9) explains that there is no issur of bal tosif when Chazal add takanos and seyagim to the mitzvos of the Torah so long as they make clear that their legislation is not a din d'oraysa. For example, the Rabbinic prohibition of eating fowl with milk is not in violation of bal tosif because Chazal never claimed that the Torah prohibited anything except animal meat and milk; they simply added an additional distinct safeguard to the existing law. Were Chazal to pretend that their enactment is actually a Torah law, they would be in violation of bal tosif.
The Ra'avad disagrees and holds that bal tosif does not apply to any Rabbinic enactments, whether they are permanent or temporary, whether they are formulated as if they were Torah law or not. What is an asmachta, asks the Ra'avad, if not an attempt to present Rabbinic law as if it was Torah mandated? (The Ra'avad clearly sees asmachta as more than a mnemonic device, in contrast to the Ritva in Eiruvin). Bal tosif applies only to individuals in their performance of mitzvos, e.g. adding extra fringes to tzitzis, an extra compartment to tefillin, extra species to one's lulav.
One thing gained by the Rambam's approach is it makes bal tigra much easier to understand -- Chazal cannot legislate away a mitzvah. If we focus on the individual's performance of mitzvos, like the Ra'avad, how is bal tigra different than a simple failure to perform a mitzvah?
Putting that point aside for now, we can explain the two views with the following chakira (Avi Ezri, Hil Mamrim): does bal tosif / bal tigra limit modification to the chiyuv or the kiyum of mitzvos? The Rambam emphasizes the immutability of Torah chiyuv or issur obligations even through Rabbinic legislation -- the nature of law itself is not subject to change. Ra'avad, however, shifts the discussion from the nature of law in theory (chiyuv) to its to fulfillment in practice (kiyum) -- has the individual performed what the Torah demanded without adding or subtracting from what is required?
As we shall see, this issue comes up in other areas as well, notably with respect to shofar.