Generally there are three places in written music where a tie will be needed.
- Where there is no note shape for a particular note length, as in duration one and three quarter beats. This could be written as a one beat tied to a half beat tied to a quarter (crotchet - quaver- semiquaver).(Yes, I know about double dots, but that's not my point).
- Where a long note lasts more than a whole bar. This could be a 6 beat note in 4/4 time, where a semibreve will be tied to a minim.(4 beat - 2 beat)
- Sadly going out of fashion, where there's for instance, a 2 beat note lasting from beat 2 to beat 3 in a 4/4 bar.This bar may be written crotchet - crotchet tied to crotchet - crotchet. The idea being in 4/4 any bar can be split visually into half. This idea shows up 'push' notes.
Rests, on the other hand, are exactly what they say - a 1 beat rest is 1 beat's worth of silence and silence is so important in music.
With guitar, sometimes the rest is superfluous as the note played previously has decayed to silence anyway, and the same thing in reverse with long notes shown with ties.