A fixed rate stays put for the entire life of the loan; a variable rate resets periodically against an index (TIIE, Cetes). In Mexico, almost no lender offers variable because the average borrower prefers certainty — most mortgages are fixed-rate, and that's already baked into the CAT (Costo Anual Total — Mexico's all-in annual cost figure) you see.
Fixed rate: your payment doesn't move for the life of the loan, whatever happens to the TIIE. Variable rate: it recalculates when the reference index changes, so your payment can rise or fall. In Mexico, consumer credit is almost all fixed; variable lives in TIIE-indexed mortgages and business credit.
How to decide: if you think rates will fall and can stomach volatility, variable can end up cheaper. If you want to sleep easy and budget exactly over 20 years, fixed. Ask explicitly before signing: «is it fixed for 36 months or variable indexed to TIIE?» — the difference can matter a lot over three years if the rate cycle turns.