Does a kicked spell count as a different spell for effects that care about mana value?

A spell's mana value (formerly "converted mana cost") is always determined solely by the mana symbols in its printed mana cost, as stated in CR 202.3. Kicker is an additional cost defined under CR 702.33, and additional costs paid do not change a spell's mana value while it is on the stack or anywhere else.

This means that if you kick a spell, effects that care about mana value — such as cost reducers, counters that reference mana value, or triggers that check "if a spell with mana value 4 or greater was cast" — will see only the base printed mana cost, not the total amount you actually paid.

There is one narrow exception: X spells. For spells with {X} in their mana cost, the value chosen for X is included when calculating mana value while the spell is on the stack (CR 202.3e). But kicker costs are never part of the printed mana cost, so they are never factored in.

Concrete example: You cast Rishkar's Expertise (mana cost {4}{G}{G}, mana value 6) kicked with an additional {3}. You paid 9 mana total, but any effect that checks the mana value of the spell on the stack — say, a trigger that fires whenever a spell with mana value 7 or greater is cast — will still see a mana value of 6, not 9.

Similarly, once a kicked permanent resolves and is on the battlefield, its mana value is still derived from its printed mana cost (CR 202.3). The kicker cost simply does not factor into mana value at any zone.