Just FYI, the starter relay/solenoid has absolutely zero to do with the alternator and charging system. It's only jobs are:
1. Energizing the starter
2. Acting as a convenient power distribution point
3. Giving a secondary boost to the ignition coil on old-school ignitions.
4. Reducing the electrical load on the ignition switch.
The alternator output wire does connect to the battery there, but it's a direct connection so the relay is acting only in it's capacity as a distribution point. The red battery cable and black charge wire are physically connected, so the relay is nothing more than a common mounting point so they can touch.
For testing the alternator, IF you can get a test probe on to the back while the engine is running (this would probably be a bad idea from an OSHA standpoint!) you want to see that same 14-15 volts.
If all of your wiring is good, the voltage you see at the battery, at the Black charge wire on the starter relay, the back of the alternator and anywhere else you test should be the same.
Or at least within a volt of the same. Frankly, any more than a 1/2v drop at different places deserves a second look.
In the reverse of that test, with the engine OFF you should see battery voltage on the BAT post and Black w/yellow wire at the back of the alternator. It's a 10ga direct connection to the battery, so should have that same less-than-half-volt drop between what you measure at the battery with the engine off and what you measure at the back of the alternator. Less drop is better and that 10ga wire should give you full battery voltage I would think.
Paul