Some spells for a wizard state that they need an ability check vs spell save DC (SSDC). I'm not understanding how this is supposed to work.

If the spell says a creature can see through the effect if it passes an Int vs the SSDC, how does that work? A d20 is rolled by DM and the Int mod (if any) of the creature is added and it has to beat (be greater than [or equal to?]) my wizard's SSDC (8+Wis mod+Prof)?

Note that this is not about how to calculate this SSDC, I already know how to do that.

Some spells for a wizard state that they need an ability check vs. spell save DC (SSDC). I'm not understanding how this is supposed to work.

If the spell says a creature can see through the effect if it passes an Int vs. the SSDC, how does that work? A d20 is rolled by the DM and the Int mod (if any) of the creature is added and it has to beat (be greater than [or equal to?]) my wizard's SSDC (8 + Wis mod + proficiency bonus)?

Note that this is not about how to calculate this SSDC; I already know how to do that.

Some spells for a wizard state that they need an ability check vs spell save DC (SSDC). I'm not understanding how this is supposed to work.

If the spell says a creature can see through the effect if it passes an Int vs the SSDC, how does that work? A d20 is rolled by DM and the Int mod (if any) of the creature is added and it has to beat (be greater than [or equal to?]) my wizard's SSDC (8+Int mod+Prof)?

Note that this is not about how to calculate this SSDC, I already know how to do that.

Some spells for a wizard state that they need an ability check vs spell save DC (SSDC). I'm not understanding how this is supposed to work.

If the spell says a creature can see through the effect if it passes an Int vs the SSDC, how does that work? A d20 is rolled by DM and the Int mod (if any) of the creature is added and it has to beat (be greater than [or equal to?]) my wizard's SSDC (8+Wis mod+Prof)?

Note that this is not about how to calculate this SSDC, I already know how to do that.

Some spells for a wizard state that they need an ability check vs spell save DC (SSDC). I'm not understanding how this is supposed to work.

If the spell says a creature can see through the effect if it passes an Int vs the SSDC, how does that work? A d20 is rolled by DM and the Int mod (if any) of the creature is added and it has to beat (be greater than [or equal to?]) my wizard's SSDC (8+Wis mod+Prof)?

Note that this is not about how to calculate this SSDC, I already know how to do that.

Some spells for a wizard state that they need an ability check vs spell save DC (SSDC). I'm not understanding how this is supposed to work.

If the spell says a creature can see through the effect if it passes an Int vs the SSDC, how does that work? A d20 is rolled by DM and the Int mod (if any) of the creature is added and it has to beat (be greater than [or equal to?]) my wizard's SSDC (8+Int mod+Prof)?

Note that this is not about how to calculate this SSDC, I already know how to do that.