[Noob MIDI question] How to hook up a sequencer?

Before everybody shoots me down with the sidebar, I have read the "Midi for Dummies" post!

That post mentions that you hook up the MIDI in and MIDI out of a sequencer, but a lot of the cheaper sequencers I see (Arturia Beatstep, Korg SQ-1, etc) only seem to have MIDI outputs (no in)? And I see YouTube videos of people using these sequencers without a computer (unless the computer was off-screen).

I tried reading the operating manuals for these and it seems to me that these sequencers don't take input, rather you determine the notes on the sequencer itself and it will output the pattern to the synth. Is this how it works? If so, I assume you can't do live recording with these sequencers, right? What about chords? Can you work chords into a sequence without an input into the sequencer?

I also read the manual to some synths, and they also mention hooking up both the MIDI in AND out to the sequencer. Will these synths still work with just the MIDI input?

Thanks in advance!