Talking about "vertical" plan (altitudes, flight level) and "horizontal" plan (positions, way points), according to the standard phraseology FAA/ICAO, is there any difference, in the usage of, between TO CROSS and TO PASS?
When related to a significant point, there is no difference between pass and cross. For altitude/FL only pass is used.
The phraselogies used by ATC is described in ICAO Doc 4444 (Air Traffic Management / PANS-ATM), chapter 12, phraseologies. The document explains the meaning for ATC, therefore to be understood and used by pilots.
18.104.22.168 LEVEL CHANGES, REPORTS AND RATES
- EXPEDITE CLIMB (or DESCENT) [UNTIL PASSING (level)]
- AFTER PASSING (significant point)
22.214.171.124 TRANSFER OF CONTROL AND / OR FREQUENCY CHANGE
- AT (or OVER) (time or place) [or WHEN] [PASSING/LEAVING/REACHING (level)] CONTACT (unit call sign) (frequency)
126.96.36.199 ADDITIONAL REPORTS
- REPORT PASSING (significant point)
- REPORT PASSING (three digits) RADIAL (name of VOR) VOR
188.8.131.52 MAINTENANCE OF SPECIFIED LEVELS
- MAINTAIN (level) UNTIL PASSING (significant point)
- MAINTAIN (level) UNTIL (minutes) AFTER PASSING (significant point)
184.108.40.206 SPECIFICATION OF CRUISING LEVELS
- CROSS (significant point) AT ( or ABOVE, or BELOW)
- CROSS (distance) MILES, (GNSS or DME) [(direction)] OF (name of DME station) OR (distance) [(direction)] OF (significant point) AT (or ABOVE or BELOW) (level)
220.127.116.11 SEPARATION INSTRUCTIONS
- CROSS (significant point) AT (time) [OR LATER (or OR BEFORE)]
- ADVISE IF ABLE TO CROSS (significant point) AT (time or level)
18.104.22.168 DEPARTURE INSTRUCTIONS
- AFTER REACHING (or PASSING) (level or significant point) ( instructions)
22.214.171.124 TURN OR CLIMB INSTRUCTIONS AFTER TAKE-OFF
- AFTER PASSING (level) (instructions)
126.96.36.199 PARALLEL APPROACHES
- YOU HAVE CROSSED THE LOCALIZER (or GBAS/SBAS/MLS FINAL APPROACH COURSE)
If another wording is used in some country, the differences must be explained in the country AIP, at section GEN 1.7. For USA (FAA AIP), Doc 4444 differences are found at GEN 1.7-23. There are none related.