Quick answer: Download size is how much data players download (compressed); install size is how much disk space the game takes once installed and decompressed. Install size is usually larger. Both affect players.
Download size and install size are two different measures of how big your game is, and players care about both for different reasons. Knowing the distinction helps you communicate and optimize. Here's the comparison.
What Download Size Is
Download size is how much data players actually download to get your game, the compressed package transferred over the network. It's what players wait for when installing, and it's a conversion factor: a large download loses players who won't wait or have limited bandwidth or data caps. Download size is about the cost of acquiring the game.
Because the download is compressed, download size is usually smaller than the eventual install size. Reducing it, through compression and trimming, gets more players through the door faster, since every extra gigabyte to download costs some installs.
What Install Size Is
Install size is how much disk space your game occupies once installed and decompressed on the player's device. It's usually larger than the download, because compressed assets expand when installed. Install size matters for whether players have room: a game that takes too much space may not fit, or may be uninstalled to free space.
Install size affects retention in a way download size doesn't, a player low on storage might delete a huge game. Both sizes matter, but for different reasons: download size for getting the game, install size for keeping it on the device.
Why Both Matter and How to Reduce Them
They measure different things and gate different player behaviors: download size gates whether players will wait to get the game, install size gates whether they have room to keep it. Both are worth reducing. The same techniques often help both, compressing assets, cutting unused content, since most size is textures and audio.
Reducing your biggest assets (usually textures and audio) shrinks both the download and the install. So treat download size and install size as distinct but related: optimize both by trimming and compressing your largest assets, and consider on-demand downloading to keep the initial download small even if the full install is larger.
Download size is the compressed data players download (gates whether they'll wait); install size is the disk space once installed (gates whether they have room). Install size is usually larger. Reduce both by compressing your biggest assets.