Ties and slurs
A curved line joins two or more notes. It's either a tie or a slur, and you tell them apart by what it joins.
Tie — same pitch, held as one
A tie connects two noteheads at the exact same pitch. You don't play the second one — you hold the first straight through it, as a single longer sound.
A tie is how you write a length that no single notehead can show — a five-beat note is a whole note tied to a quarter — or a note that has to carry over a barline.
Slur — different pitches, one bow
A slur curves over notes at different pitches. It's a phrasing mark, and on the violin it almost always means: play the whole group in one bow, without re-starting the sound for each note. The left-hand fingers still change; the bow just keeps travelling.
The quick test
Does the curve join two noteheads at the same height on the staff? Tie — hold it. Does it arc over notes that move up or down? Slur — one bow. A curve across a barline joining identical pitches is almost always a tie.
The usual mistake
Re-bowing or re-plucking across a tie — you get two attacks where the music wants one long note. Or reading a slur as a tie and sitting on one pitch while the tune was meant to move.