Although they share the concept of "parametric font technologies", variable fonts are a completely different expression of that than metafonts. Where a metafont glyph is programmatic (complex, but great flexibility and control), a variable font glyph is mostly declaritive (simpler and more accessible, but less flexible in some respects), consisting of a set of variations with defined axes to control how the variations should be interpolated/tweened to control properties like weight, width, slant, etc.

A good overview of variable fonts is "Introducing OpenType Variable Fonts" (2016): https://medium.com/variable-fonts/https-medium-com-tiro-intr...