Some confusion might come from the the designation "Lee Speed". Lee Speed is the actual name of the rifle family. It comes from the engineers who designed it, James Lee and Corporal Joseph Speed. When it was adopted by the Britishicon, the enlisted Speed's credit was given to Enfield RASF, hence all British government Lees are Lee Enfields.

For the commercial production, manufacturers were allowed to properly credit Speed. All rifles produced as sporter, target, and foreign military patterns are Lee Speeds.

There are several variants of commercial rifle at this time, but for the sake of simplicity, it can be narrowed down to two. Customers can choose if they wanted cleaner stronger Enfield rifling, or weaker accurate Metford rifling for either variant. Commercial metford barreled rifles will have the No 1 Lee Speed action, without a E marked on the barrel.
The first is a sporting pattern. This is a shorter rifle without full wood. May not look much different than a sporterized SMLE, but very rare and desirable.
The second is the military model. These are almost exactly the same as produced for the British. The Ethiopian hoard is made up of these.