Suggestion: It appears that relevant references are needed or required in practical situations. In some cases, the textbook approach is allowed in others industry standards, military standards, safety codes, etc. must be followed or preferred.
The rhatcher postings above may be supplemented/corrected (marked by >>) as follows:
Vab = line-to-line voltage or line voltage
>>or phase-to-phase voltage
Van = line-to-neutral voltage or phase voltage
>>or phase-to-neutral voltage
Ina = phase current
>>or phase-to-neutral (line-to-neutral) current
Iax = line current
Note that for a wye
Ina=Iax (phase current=line current always)
Vab=Van*sqrt3 (balanced 3 phase only)
>>Addition: In case of phase-to-phase (or synonymously, line-to-line) fault, there is phase-to-phase (line-to-line) fault current
Doing the same exercise with a delta generator yields the following:
Vab=line-to-line or line voltage
>> or phase-to-phase voltage
Iab=phase current
>>Correction: Phase-to-phase (or line-to-line) current
Iax=line current
>>or phase current
Note that for a delta
no neutral

hase voltage=line voltage (always)
>>phase-to-phase voltage=line-to-line voltage (since there may be considered a fictitious neutral for analyses, etc.
Iax=Iab*sqrt3 (balanced 3 phase only)
Loads are similarly named, with a wye being
Zan=phase impedance
>>phase-to-neutral (or line-to-neutral) impedance
Zab=line impedance
>>or phase-to-phase (or line-to-line) impedance
Ian=phase current....etc.
>>or phase-to-neutral (line-to-neutral) current
Reference:
1. ANSI/IEEE Std 242-1986 "An American National Standard IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems"
Reference 1, page 115 states that "A current transformer transforms line current into values suitable for standard protective relays...." Since the current transformers may be connected in delta- or y-connection, as needed or required, then the line is interpreted as the line-to-neutral (phase-to-neutral) current for y-connection and line-to-line (phase-to-phase) current for the delta-connection. This agrees with my first posting and does not contradict the Reference 1 intent. Good references tend to remove a lot of subjectivity in postings. Also, the ground fault current subject is more involved, e.g. there are line-to-line-to-ground faults that are different from line-to-ground faults.