(In case you didn't know,) I am Ashkenazic. Most Ashkenazic congregations perform Torah reading by laying the Torah flatly on a table and reading the Torah as it is on the table.
Many Sefardic communities have beautiful encased Torah scrolls and the Torah is read with the case standing vertically on the table.
What is the origin and reason for these differences?
The Taz says that if he is ever zocheh to write a Sefer Torah and build an Aron Kodesh, he would build it wide enough to put the Sefer Torah lying down and that is also the seder kriyaso.
This means:
When we speak about the placement of kisvei hakodesh, not only does the halochah apply to mezuzah and tefillin, but the Taz extends this to Sifrei Torah as well. Therefore, in places of Edut HaMizrach, where the Mezuzos are standing according to Rashi and the Rambam, the Sefer Torah has to be standing. How do you make a Sefer Torah able to stand? You put it in a box. Therefore, their Sifrei Torah are placed in a box and they're standing on a bimah which is straight and horizontal. In this way they can read the Sefer Torah completely vertical, which is completely kisvei hakodesh.
Therefore, with Ashkenazim, who have their mezuzos slanted, their bimahs should be slanted, and really, this means that their Sifrei Torah are read slanted in accordance with the Rema.
Interestingly, the Morrocan minhag is to have the Sefer Torah on polls which are on a bimah which is slanted because they, like the Ashkenazim, have their mezuzos slanted. In this way their Sifrei Torah are read standing in accordance with kisvei hakodesh and slanted in accordance with the Rema.
