Should variations of a color, within a color palette, only consist of tints and shades of that color?

I'm designing an IDE with dark UI. We have an existing color palette, but our (~10) greys seem off when applied to the IDE in the large quantities dark UI calls for.

When analysing each swatch, I realised that they don't belong to one HTML color family. Should variations of one color, within a good color palette, not consist of tints and shades of the same color or color family?

To add to my confusion, both Material Design (https://material.io/resources/color/#!/?view.left=0&view.right=0&primary.color=263238) and Human Interface Guidelines (https://developer.apple.com/design/human-interface-guidelines/ios/visual-design/color/) contain grey palettes with greys from different HTML color families.