Yes, it is true that they both "contain" Lithium in them and in each charge and discharge cycle Lithium ions move from one electrode to the other and there are also 'free' Lithium ions in the electrolyte between the Anode and Cathode. However, whereas in what is generally known as a regular Li-ion cell there are also other exotic metals (i.e. Nickel and Cobalt) to enable those ions to move to and fro and to provide a home for those "Li" ions, the LEP has Iron (fe) and Phosphorous (P) instead of Nickel (Ni) and Cobalt (Co) and consequentially a less flammable electrolyte into the bargain.
Whilst there is a constant development to modify the structure and Li-ion chemistry, the Li-ion battery remains essentially the same and uses Ni and Co and continues to be referred to as Li-ion since its cell characteristics and voltage range etc. is defined by that Li-Ni-Co chemistry. There are variants of this chemistry which have very low Cobalt content or even Colbalt free, however, they still exhibit the Li-ion characteristics. Whereas an LEP cell, with Li-fePo4 derived chemistry, will have distinctly lower cell voltages and different charge/discharge profiles.
Hence the LEP deserves to be characterised as different just as an ICE driver needs to know whether they are driving a Petrol or Diesel fueled car before refuelling so the EV driver/owner ought to be told about the battery tech since they need to be treated differently for optimum performance and longevity of the most expensive part of their investment.