Charging 12 V 7 Ah lead acid battery
The thing you're missing is that your 14v power supply can output enough current to charge the battery and keep the terminal voltage at 14v. Your solar panel clearly does not output enough current, and the battery is taking all the charging current it can provide at 13v.

If you want to charge the battery with the panel, it will take as long as it takes. Get a bigger panel, or more light on the one you have, if you want it to charge faster, with that simple circuit. It may be possible to squeeze a higher charge rate if you used a MPPT converter, to operate the panel at its best power output point, which may not be 13v.

That said, the 1N4007 will drop a volt, a pretty wasteful form of protection, a MOSFET that can be switched on would be far better.