The gemara says that one who is studying Torah must stop for Krias Shema, but for davening one must only stop if he is not "toraso u'mnaso" - meaning that he stops learning to work, to the exclusion of R. Shimon Bar Yochai who was toraso u'mnaso would not stop learning for davening. Rashi explains that the difference between shema and davening is that shema is d'oraysa to be read within certain times whereas the times for tefillah are only d'rabonon [Rashi implies that he holds like the Rambam that davening everyday is d'oraysa, just that the z'man tefila is what R. Shimon Bar Yochai was allowed to miss since it is only d'rabonon]. The Ran points out that although in the context of the beginning of the mishna regarding work, one must stop before missing the z'man tefillah, in the context of studying Torah the אין מפסיקין means that you don't need to stop even if you are going to miss the time. The Ran proves this from the fact that we only allow this for one who is torasa u'mnaso and not for others. If we were speaking about stopping Torah study even when there is time to daven later, even one who is not toraso u'mnaso can continue studying and doesn't need to stop - ואי בדאיכא שהות, כגון אנו למה מפסיקין, וכי אסור לעסוק בתורה קודם שיתפלל. The Ran takes for granted that there is no prohibition to learn before davening. However, in Brachos 5b, Rashi seems to say that there is a prohibition to learn before davening, and Tosafos there takes issue with that and assumes like the Ran.
What is the rationale to distinguish between those who are תורתן אומנתן and those who are not torasan u'mnasan? Rashi writes that those who stop for other activities such as work, must also stop for davening. This can be explained in two ways: 1. The Chofetz Chaim in Shemiras Halashon in a note writes that just as when it comes to issurim we find a concept of achashevei, which means that something inedible that you eat and give chashivus to, is considered food, here too. Those who refuse to stop learning to earn a living and are achshevei their Torah study to give it such value, it truly has more value and becomes more important than tefillah. But for those who don't give their Torah that level of chashivus, it is considered to be worth less than tefilla so they must stop to daven. 2. I would like to suggest another approach based on the gemara 10a that considers tefillah to be chayei sha'ah since one is praying for physical needs on this world, to the exclusion of Torah which is chayei olam since it is purely spiritual. Those who are involved only in chayei olam i.e. Torah, have the right to ignore chayei sha'ah i.e. tefillah. But those who break from their chayei olam to work and earn a living, since they take very physical and mundane steps to worry about their chayei sha'ah, they are obligated to also take spiritual steps to worry about chayei sha'ah. Since they stop learning to work for chayei sha'ah, they must daven for chayei sha'ah also to put things in perspective and recognize that their parnasah is from Hashem.