Technically trackers are a type of sequencer. A sequencer (as it first was called in the old days) is typically a device that will allow you to arrange notes in a sequence (one note after the other) for automatic playback. It doesn't actually record any sound. It just sends a signal (MIDI, CV-gate, etc.) to an external electronic instrument, which then instantly plays that note.
The earliest sequencers tended to be pattern-based ones. The very earliest ones just played repeating bass patterns or arpeggios. Then when MIDI came around you didn't have to press buttons on the sequencer anymore to enter data, you could enter data through a MIDI keyboard.
These early sequencers were hardware boxes that would record your MIDI data. Esentially they were little stand-alone computers that just did one job. Later when home computers became popular, sequencing software was written for those platforms. With this early hardware and software you could arrange short patterns, one for your chorus, one for your verse, etc. and then arrange the patterns to have a song.
As sequencers got better, you could enter more notes, and even have multiple "tracks" that would hold MIDI data. Like multi-track tape, you could then alter one "track" without ruining the other sequencer's tracks.
The thing about sequencing software is that the modern stuff doesn't resemble the early stuff very much. It has evolved from manipulating raw MIDI code (like DR.T's KCS) to something more visual....displaying the MIDI data as colourful "tracks" you can see and manipulate with a mouse. Bar's & Pipes is like this. The screen is layed out with all the tracks neatly stacked, and as you record or play, the tracks scroll by and the notes are represented by coloured lines.
I wouldn't call Deluxe Music construction set a sequencer. It's more of a notation editor (uses staff based notation) which can also play the notation back via MIDI.
Because trackers approach sequencing in a very unique way, they are sort of grouped seperately from normal sequencing software. They are a little more limited than your normal sequencer...but they are designed to do computer music very well. They all display the data for channels in columns, and you enter codes for specific notes & events at certain points along a fairly rigid time line (like 64 pulses per beat or something). Trackers are also (at least in the beginning) tied closely to the hardware they are programmed on (i.e. the sound chips of the Amiga or C64). Only later did they start implementing MIDI (and hence became closer to general sequencers).
So, we've got the following classes of music software:
1. Sequencers (Play in MIDI notes from a keyboard, re-arrange it, and have it play back):- Bars & Pipes, Music-X, Dr. T's KCS, Camoflage, etc.
2. (really a subset of 1) Trackers: (Type in MIDI events or sample trigger events on a rigid 4/4 type cycle and arrange patterns for playback):- OctaMED, MED Sound Studio, Protracker, etc.
3. Multitrack recording software (DAW): (Record, mix, and EQ real audio):- Audio Evolution, HD-REC, ProStation Audio.
4. Notation editors: (Shuffle around music notation and print out nice scores for other musicians to read):- Deluxe Music Construction Set.
However, the lines are blurring between all these as the software becomes more advanced. Bars & Pipes will allow you to display the music as real notatation, print it, and even trigger samples. HD-REC supposedly has a built-in Bars & Pipes like MIDI sequencer.
It's just like the way word processors used to be raw ASCII editors but now are taking on some of the features of Desktop Publishing / Image manipulation / Web authoring software.
For your purposes (sound recording only) I would try HD-REC. It think the beta version is free right now. The other programs are good, but are expensive and might be a bit of an overkill until you get more experienced.
You could also try Samplitude, which is free. It has a limited multitracking ability. I'm not sure how well it works for full duplex recording (i.e. listening to the other tracks while you play along and record).