Is there a difference between "Al-Basmalah" and "Al-Tasmiah," and is one of them recited upon entering the restroom or when beginning any matter?

"Basmalah" is a verbal noun derived from "basmala," meaning "to say 'Bismillah'." It is a word formed by naḥt (clipping) for conciseness. As for "tasmiyah," it is a verbal noun derived from "sammā" (to name). There is no difference between our saying "basmalah" and "tasmiyah," as both mean "to say 'Bismillah'" or "Bismillah ar-Rahman ar-Rahim." The basmalah is recommended at the beginning of every important matter, based on the Prophet's (peace and blessings be upon him) saying: "Every important matter that does not begin with the remembrance of Allah and with 'Bismillah ar-Rahman ar-Rahim' is cut off [of blessings]."