Date: 201811
Local time of day: 1801-2400
Location: SLC.Airport, UT
Flight conditions: VMC
Light: Dusk
Aircraft: Light Transport; Low Wing; 2 Turbojet Eng
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class B SLC
ATC / advisory: TRACON S56
Second aircraft: Bombardier/Canadair Undifferentiated or Other Model
Reporter organization: Corporate
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Commercial
Human factors: Communication Breakdown; Distraction
Second reporter function: Approach
Anomaly: Conflict Airborne Conflict; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Returned To Clearance
Contributing factors: Human Factors; Procedure
Primary problem: Human Factors

Narrative: We departed SLC on Runway 35 on the ARCHZ1 departure for ZZZ. We briefed our departure instructions and performed our route verification and all SOP's were complied with. The ARCHZ1 departure states assigned heading of 260 degrees for radar vectors to the first fix (SCANT intersection); cross above 10;000 feet and the top altitude is FL230. On departure we turned to the ATC assigned heading of 260 and we were climbing at a quick rate of 230 knots as assigned via our ATC clearance via ACARS. As I was passing through 10;000 feet we received a 'Traffic' alert from the TCAS. My first thought was we shouldn't be getting a 'Traffic Alert' and I reduced my climb rate. A few seconds later we received crossing traffic advisories from ATC and I quickly picked both targets up visually in my scan. We continued our climb and I keep thinking this departure didn't make sense with respect to the crossing traffic and our altitude. Moments later ATC cleared us to FL230. That's when I knew something wasn't right and we may have made a mistake. Soon after SLC cleared us a Center frequency and we continued on our way landing in ZZZ without incident. Once we leveled off I asked my partner to review our clearance and the SID. We found our mistake. Due to limitations of the Garmin ACARS system and the fact that ATC issues clearances via ACARS in no standard format we missed in our departure instructions our initial altitude level off of 10;000 feet.  We were cleared the ARCHZ1 departure and assigned an airspeed of 230 knot. The airspeed came before the or where the altitude portion of the clearance is usually published. This was confusing and we missed it. Also; coincidentally; the initial altitude published on the ARCHZ1 departure is FL230. The way the clearance was submitted and there being no standard format was a contributing factor to us missing the 10;000 foot clearance limit. The word EXCEPT in the ALT line would have helped us with our mistake. Also the 230 knot speed limit and the FL230 altitude on the SID created a chance for confusion. We never received a TA or RA on departure and I am not sure if ATC saw we didn't level off at 10;000 feet as our clearance called for. No threat between us or other aircraft existed but it could have during a busier time period. A standard format in which all ACARS clearances is a must to prevent errors in the future. Standard or universal clearances via ACARS between all ATC outlets.


Second narrative: Aircraft X checked in at '095 for 230'. He should have been stopped at 100 for the downwind traffic at 110. I did not hear 230 on his check-in and issued traffic but did not correct the altitude. He lost separation with Aircraft Y in the downwind at 110.  Not missing altitudes pilots say.


Synopsis: Corporate pilot and Air Traffic Controller reported a missed crossing restriction resulted in a loss of separation.