A sequencer is a box that allows to record/program and playback a series of midimessages. Midi messages include such things as note on (with parameters to say how loud and which notes), note off, .... Most sequencers come with a built-in soundsource, mostly sampleROM based (samples in ROM, you cannot change them), but a built-in soundsource is not required.
A synthesizer is something that allows the user to synthesize waveforms. In musical context that means, it allows you to make sounds. This can be done in different ways... Subtractive synthesis is the most common. You start with an oscilator, the output of that goes thru a filter, and is amplified using a certain envelope as modulating input for the amplifier. Today these things are simulated digitally.
Some synths are ROM based. They synthesize sounds originating from a sample in a rom. But this is rather close to what we would call a rompler; a soundsource that just plays back samples, which can be edited a little using effects of some sort and some modulation.
Then there's a sampler. Which is basically the same as a rompler, with this difference that the samples aren't burnt in a rom, but can be changed, recorded yourself and edited....
Currently I have a Technics P-50 keyboard, and I want to add drums to my music or percussion stuff, how will I go about doing so?