Pick the right size before you export
An SVG has no fixed resolution, so the PNG is drawn fresh at whatever size you ask for. For app icons and retina screens export at 2× or 3× the size it will be displayed at. For print, multiply inches by 300: a 2-inch logo needs a 600 px wide PNG.
Why some SVGs render differently
Browsers draw SVG inside an <img> context without access to external files. If your SVG links to a web font, an external image or a CSS file, those parts will be missing. Convert text to outlines in your design tool, or embed images as data URIs, before exporting.