As said above, completely different things.
Category L2 related to non domestic fire alarm systems and is the one before the top layer of detection provision - it incorporates manual call points and sounders (M), Escape routes (L4), rooms opening onto escape routes (L3) and covers other specific risks identified in the system design (i.e. no fixed criteria, in theory you could have two identical buildings both with L2 systems, one having 2 extra detectors to locations not covered by L3 and the other having 22 extra detectors covering a wider range of areas. Usually it's places like motor rooms, plant rooms, electrical intakes, kitchens and the like but doesn't have to be).
Grade relates to domestic fire alarm systems, the ones most familiar to most people being the Grades F (battery only, subdivided into tamper proof and user changeable types) and D (mains with back up battery, also subdivided between tamper and non tamperproof). Grade A is where the same equipment as used on commercial systems is used however whilst the design & installation requirements are similar they are not the same with a small number of differences.
The life safety categories for domestic systems are LD1, 2 & 3 which whilst similar in principle to the L categories are very different in where they go being based on house/flat layouts and instead of starting with manual call points as in commercial systems, they usually only come in at the highest grade of system.
Things can be more confusing as depending on the type of premises and reason for installation you can have a commercial BS5839-1 'L' category system type installation of panel, call points, detectors and sounders (e.g. purpose built flats needing evacuation strategy or sheltered housing) or the same equipment but installed & designed as a domestic BS5839-6 Grade A 'LD' category system (e.g. large HMO's, certain conversions of houses to flats)
