The avatar is of a lower resolution on the desktop client than on the mobile client.

As the undermentioned demonstrate:

1. https://www.reddit.com/r/discordapp/comments/zvwhl0/avatars_are_blurrylowquality_on_desktop/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button
2. https://www.reddit.com/r/discordapp/comments/15mhyy4/low_quality_pfp_on_pc_but_looks_fine_on_mobile/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button
3. https://www.reddit.com/r/discordapp/comments/12i2jt4/blurry_profile_picture/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button
4. https://www.reddit.com/r/discordapp/comments/6jvo2z/low_quality_discord_profile_picture/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

…and my own anecdotal corroboration, the avatar is rendered at a lower resolution on the desktop client than on the mobile client.