Ideally, the same text should appear consistent across any UI. Obviously, some apps will use different fonts and colors and may interpret the style of an element differently.
Oh yea styling isn’t the issue here … it’s whether the markdown is correctly interpreted and rendered. AFAIU, lemmy doesn’t have any instructions about how to interpret the text, just some standard that they’ve chosen to use, along with their open source software for doing so (as they’ve built too clients, the default web UI and Jerboa).