An aspect ratio is just a simplified ratio of width to height -- 16:9, 4:3, 1:1, 9:16. The same ratio can apply to wildly different actual resolutions: a 1920x1080 video and a 3840x2160 (4K) video are both 16:9. What changes between formats isn't the shape, it's how many pixels fill that shape.
Why you can't fit one ratio inside another without cropping
Converting 16:9 footage to 9:16 for a vertical feed isn't a resize -- it's a crop, because the two shapes don't share the same proportions. Either you crop the sides off the original frame (losing width) and keep full height, or you letterbox it with blank bars to preserve the full original frame inside the new shape. There is no lossless way to turn a wide rectangle into a tall one without giving up part of the image or adding padding.
Resolution vs. aspect ratio vs. PPI
These three numbers answer different questions. Aspect ratio is the shape (width:height). Resolution is the pixel count (1920x1080). PPI (pixels per inch) is how densely those pixels are packed when printed or displayed at a physical size -- the same 1920x1080 image has a much higher PPI printed at 4x6 inches than blown up to a 24x36 inch poster, even though the resolution and aspect ratio haven't changed at all.
Confusing these is why 'this photo isn't high enough resolution to print large' and 'this photo is the wrong shape for this frame' are two completely different problems with two completely different fixes.
Planning ahead instead of fixing it after
If you know a photo or video needs to end up in a specific aspect ratio, it is almost always easier to frame for that ratio while shooting than to crop afterward and lose part of the composition. The aspect ratio calculator converts between a target ratio and any known width or height so you can check the numbers before you shoot, not after.