Cat6 conductors are thicker (typically 23 AWG) than Cat5e conductors (typically 24 AWG).
As someone already pointed out, Cat6 plugs arrange the conductors in a staggered pattern because they can be too thick to fit side-by-side.
As far as jacks go, the thicker conductors of Cat6 cable may or may not fit in the IDCs (Insulation Displacement Connectors) of a Cat5e jack.
Most keystone-style jacks use either LSA-Plus (aka Krone) or 110 IDCs (or a very common new hybrid that accepts both types of punchdown tools). In theory both are compatible with wire up to 23 AWG (2.5mm²).
That said, there's no guarantee that every manufacturer abides by every specification of every standard but I can say that so far, the various Cat6 cables I've been using have punched down cleanly into the various hybrid-IDC Cat5e (and Cat6) jacks that I found on Amazon and elsewhere.
However, if you're building a certified network that has to operate at the highest spec possible then you're probably not shopping for parts at Amazon. You're probably using wiring, tools and connectors designed to work together as a system, probably provided by an integrator or a large company like Belden or Panduit.
The rest of us will just punch our jacks and take our chances.
Would my jacks pass a certification test? I don't own any fancy test equipment so I don't know, but they pass data with adequate speed and that's good enough for me.
Your mileage may vary.