What is a Counting Phrase™?

Question

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.}

If a phrase conforms to a special rule, I call it a Counting Phrase™.

Use the following examples below to find the rule.

Counting Phrases™	Not Counting Phrases™
RUSH IN	GET OUT
IRON MILL	SMELTING FURNACE
LONG GAME	DECISIVE VICTORY
IDLE POWER	INCREMENTAL GAME
LANE ORDER	FREE PLAY
VAPOR BATH	HOT SAUNA
EAGLE COIN	DOLLAR BUCKS
FLINT CLAY	IRON PICKAXE
JAY INSLEE	BILL HASLAM
WICKET DOOR	BAFFLE GATE
COMMON BENT	FAIRWAY TURF
MICHAEL BAY	MICHAEL FOX
GRAND COULEE	THREE GORGES
OKCUPID LOVE	TINDER MATCH
WARRIOR KING	PHILOSOPHER QUEENS
COMMUNITY PARK	INDUSTRIAL PARK
MOUNTAIN CEDAR	OLIVE GARDEN
VALENCIA ORANGE	BLOOD ORANGE
TEXAS MOTORPLEX	KENTUCKY SPEEDWAY
IMPERIAL CAPITAL	TOWN CENTRE
ALTITUDE CHAMBERS	HYPERBOLIC TIME
FOUNTAIN INKSTAND	BALL POINT
CHRISTIAN MORALITY	RELIGIOUS FUNDAMENTALISM
PARTICULATE CARBON	OZONE LAYER
SCULPTURESQUE JASPER	TEXTURELESS LIMESTONE
SWITZERLAND INTERNATIONAL	NEUTRAL PARTY

And, if you want to analyze, here is a CSV version:

Counting Phrases™,Not Counting Phrases™
RUSH IN,GET OUT
IRON MILL,SMELTING FURNACE
LONG GAME,DECISIVE VICTORY
IDLE POWER,INCREMENTAL GAME
LANE ORDER,FREE PLAY
VAPOR BATH,HOT SAUNA
EAGLE COIN,DOLLAR BUCKS
FLINT CLAY,IRON PICKAXE
JAY INSLEE,BILL HASLAM
WICKET DOOR,BAFFLE GATE
COMMON BENT,FAIRWAY TURF
MICHAEL BAY,MICHAEL FOX
GRAND COULEE,THREE GORGES
OKCUPID LOVE,TINDER MATCH
WARRIOR KING,PHILOSOPHER QUEENS
COMMUNITY PARK,INDUSTRIAL PARK
MOUNTAIN CEDAR,OLIVE GARDEN
VALENCIA ORANGE,BLOOD ORANGE
TEXAS MOTORPLEX,KENTUCKY SPEEDWAY
IMPERIAL CAPITAL,TOWN CENTRE
ALTITUDE CHAMBERS,HYPERBOLIC TIME
FOUNTAIN INKSTAND,BALL POINT
CHRISTIAN MORALITY,RELIGIOUS FUNDAMENTALISM
PARTICULATE CARBON,OZONE LAYER
SCULPTURESQUE JASPER,TEXTURELESS LIMESTONE
SWITZERLAND INTERNATIONAL,NEUTRAL PARTY

Helpful changes: Added some more phrases in response to comment expressing character underrepresentation. Added knowledge tag

Hint 1:

There are two separate, but related, conditions.

Hint 2:

gnovice has one of the conditions partially figured out; the other condition is alluded to by the category name. As the tag suggests, you may want to search stuff up to confirm your findings.

Answer 1

Adding onto @gnovice's answer, the phrases must meet the following conditions:

One of the words must contain a two-letter abbreviation of a state.
The other word is a county in that state.

Listed out:

RUSH IN                   = Rush County, Indiana
IRON MILL                 = Iron County, Michigan
LONG GAME                 = Long County, Georgia
IDLE POWER                = Power County, Idaho
LANE ORDER                = Lane County, Oregon
VAPOR BATH                = Bath County, Virginia
EAGLE COIN                = Eagle County, Colorado
FLINT CLAY                = Clay County, Florida
JAY INSLEE                = Jay County, Indiana
WICKET DOOR               = Door County, Wisconsin
COMMON BENT               = Bent County, Colorado
MICHAEL BAY               = Bay County, Michigan
GRAND COULEE              = Grand County, Colorado
OKCUPID LOVE              = Love County, Oklahoma
WARRIOR KING              = King County, Washington
COMMUNITY PARK            = Park County, Colorado
MOUNTAIN CEDAR            = Cedar County, Missouri
VALENCIA ORANGE           = Orange County, Virginia
TEXAS MOTORPLEX           = Texas County, Missouri
IMPERIAL CAPITAL          = Imperial County, California
ALTITUDE CHAMBERS         = Chambers County, Alabama
FOUNTAIN INKSTAND         = Fountain County, Indiana
CHRISTIAN MORALITY        = Christian County, Missouri
PARTICULATE CARBON        = Carbon County, Pennsylvania
SCULPTURESQUE JASPER      = Jasper County, South Carolina
SWITZERLAND INTERNATIONAL = Switzerland County, Indiana

Answer 2

Partial answer

I'm fairly certain that one of the two conditions involves...

...having at least one word that starts with the two-letter abbreviation for a state. All of the Counting Phrases™ satisfy that, but only a few of the Non-Counting Phrases™ do:

RUSH IN                      GET OUT
IRON MILL                    SMELTING FURNACE
LONG GAME                    DECISIVE VICTORY
IDLE POWER                   INCREMENTAL GAME
LANE ORDER                   FREE PLAY
VAPOR BATH                   HOT SAUNA
EAGLE COIN                   DOLLAR BUCKS
FLINT CLAY                   IRON PICKAXE
JAY INSLEE                   BILL HASLAM
WICKET DOOR                  BAFFLE GATE
COMMON BENT                  FAIRWAY TURF
MICHAEL BAY                  MICHAEL FOX
GRAND COULEE                 THREE GORGES
OKCUPID LOVE                 TINDER MATCH
WARRIOR KING                 PHILOSOPHER QUEENS
COMMUNITY PARK               INDUSTRIAL PARK
MOUNTAIN CEDAR               OLIVE GARDEN
VALENCIA ORANGE              BLOOD ORANGE
TEXAS MOTORPLEX              KENTUCKY SPEEDWAY
IMPERIAL CAPITAL             TOWN CENTRE
ALTITUDE CHAMBERS            HYPERBOLIC TIME
FOUNTAIN INKSTAND            BALL POINT
CHRISTIAN MORALITY           RELIGIOUS FUNDAMENTALISM
PARTICULATE CARBON           OZONE LAYER
SCULPTURESQUE JASPER         TEXTURELESS LIMESTONE
SWITZERLAND INTERNATIONAL    NEUTRAL PARTY

I think one of the most helpful entries will be MICHAEL BAY versus MICHAEL FOX, but I haven't figured out the second condition yet.