BPM is the count. It doesn't equate to the number of notes played per minute. There could be one note that lasts for several beats or, at the other end of the scale, 32 notes played per beat.

If you're playing with a metronome set at a faster tempo than the recording but still playing slower, then that suggests you're playing notes of too long a duration (e.g. quarter notes where they should be 16th notes).