A vector has no resolution
This is the part that trips people up. An SVG is a description of shapes — curves, fills, strokes — and it can be drawn at any size with no loss. There is no "actual size" hiding inside the file.
So rasterising is not really a conversion; it is a decision. The size selector is where you make it, and it is the most important control on this page.
Pick the size for the destination: 512 or 1024 for a favicon source or an app icon, 2048 for something that will appear large on a high-density screen, and the smallest that still looks right for anything going onto a web page.
JPG has no alpha channel, so the transparent areas are filled with white. Use it only where the destination refuses PNG.
Keep the SVG
The raster is a derivative. Every time you need a different size you should go back to the SVG and rasterise again, not scale the PNG — scaling a raster up blurs it, and scaling it down repeatedly softens it.
What the browser can and cannot resolve
Fonts come from your system, so text in an SVG renders with what your machine has. Images referenced by an external URL are not fetched, because this page makes no network requests at all. An SVG with its fonts converted to paths and its images inlined will convert identically everywhere.
Questions
Why do I have to choose a size?+
Because a vector has no size of its own. An SVG icon might declare width="24", but that is a suggestion, not a resolution — the file describes shapes, not pixels. Rasterising means deciding how many pixels to draw them with, and picking 24 because the file said so would produce a useless thumbnail.
What is lost?+
Scalability, and it is the only thing that matters here. The SVG stays sharp at any size; the raster you get is sharp at one size and blurry above it. Keep the SVG — this is an export, not a replacement.
Does it handle embedded fonts and external images?+
Text renders with whatever fonts your browser can resolve, so an SVG relying on a font you do not have will look different. External images referenced by URL are not loaded, because the page makes no network requests. Convert an SVG with everything inlined for a predictable result.