Star, you are not being naive. You are learning. The meat that religiously observant people eat nowadays is Glatt kosher. Once upon a time very long ago, in the early to mid – 1900s, kosher butchers sold meat that may or may not have been considered glatt. It was to minimum standards kosher meat,to be sure, but as with all things in the religiously-observant world, it is always better to elevate ourselves in holiness in everything we do, including the food we eat, and with a new wave of immigration to these shores also came the adherence to using only glatt kosher meat.
As was explained “glatt” means smooth(referring to the lungs), and though some scabs in the lungs of a cow, which often inhales small stones as the cow grazes and chews its cud) do not render it as a “treif” animal, since some scabs that form from the irritation to the lungs ARE going to render the animal treif, the meat of a questionable animal is never sold as glatt kosher, and therefore not used by reputable kosher butchers for sale to observant Jews. When there is no glatt label, it cannot be ascertained that the meat is acceptable even by minimal kosher standards.
Today’s standards of kashrus are higher and virtually no frum person I know of would consider eating meat that is not certifiably glatt kosher. AND the butchers who call their non- glatt meat kosher are most likely not frum Jews altogether, or they would not be selling meat that is non-glatt to kosher consumers for the reasons stated above.
I can understand the frustration at having to look for a greater expense with fewer options rather than buying your meat from Tomer, BUT you have made the difficult decision to be a Jew, and if your honest intent is to be kosher, the non-Glatt company is NOT the one from which to buy your meat. Unless the meat is under reliable Kashrus supervision, you cannot depend on Tomer, or anyone else regarding its kashrus.
But this forum is not the best place for you to seek advice in this regard. Speak to the Rov who is involved in teaching you about the laws of Kashrus, and see what he advises you to do at this point, the early stages of your conversion process. I am making the assumption that the rabbi helping you on your spiritual journey is unquestionably a Torah-true scholar, not a Conservative or Reform practicioner. I wish you success.