I don't know what confusion of ideas created your current state of mind, but a reduction in tax is not a subsidy.
The maximum benefit to the economy is achieved when economic distortion due to tax or subsidy is zero.
Consider the traditional supply vs demand plot:
$| \D S/ In an undistorted market,
| \ / the equilibrium point where
| \ / D and S intersect determine
A|----X the price (A) and quantity (B)
| /|\ that will be sold.
| / | \
| / | \
+---------
B #
The consumer benefit to trade is the area
below D and
above A. The producer benefit to trade is the area
below A and
above S.
$| \D S/ In a taxed market, the tax
C|--\ / creates a difference between
| |\ / what the consumer pays (C) and
A| | X what the producer gets (E).
| |/ \ As a result, the quantity sold
E|--/ \ drops to a lower value (F).
| /| \
+---------
F B #
The tax revenue is the area
above E,
below C, and
left of F. It is possible this can be returned to the economy intact, if the government spends it wisely. The triangle of the former benefit of trade to the
right of F and
left of B is
deadweight loss, and is lost forever. The new consumer benefit is
above C and
below D, while the new producer benefit is
below E and
above S.
$| \D S/ In a subsidized market, the subsidy
G|--\---/ creates a difference between
| \ /| what the consumer pays (H) and
A| X | what the producer gets (G).
| / \| As a result, the quantity sold
H|--/---\ increases to a higher value (I).
| / |\
+---------
B I #
The cost of the subsidy is the area
below G,
above H, and
left of I. This produces an additional consumer benefit
below A and D, and
above H, and additional producer benefit
above A and S, and
below G. Note that this produces another triangular area of deadweight loss that the government spends to produce zero additional economic benefit.
In conclusion, a reduction in tax cannot in any way be reasonably considered equivalent to a subsidy.