The difference in FMJ and TMJ is the TMJ totally encapsulates the lead core. This is to prevent exposure to lead during loading and shooting. FMJ has a jacket into which a lead core is swaged, leaving the back end of the bullet with exposed lead.
Don't worry at all about the weight. +/- 1 grain means nothing.
TMJ I believe are always plated bullets. These require slightly lower velocities to prevent the plating from becoming separated from the core at high speeds. The manufacturers usually recommend keeping velocity under 1100 fps so any load not over that should work well.