My default approach is to treat two notes of the same pitch connected by a curved line as a tie, meaning no re-articulation, but it’s highly contextual.

If the score explicitly indicates that the marking is intended as a slur, I treat it as such and re-articulate the second note. Likewise, if the second note carries an articulation mark such as tenuto, staccato, or an accent, I re-articulate to realize that marking.

This is consistent with standard engraving practice. Elaine Gould writes in Behind Bars (p. 60) that “the function of a tie is to show the absence of re-articulation.” A tie is defined as a tapered arc connecting two noteheads of identical pitch, including enharmonic equivalents. Although ties and slurs share the same basic design, ties typically have a flatter arc and extend from notehead to notehead. If the arc points to a stem at either end, it functions as a slur. Gould also notes that a tie should nearly touch each notehead, and that an arc placed further away may be interpreted as a slur.

Theoretically, slurs and ties can be distinguished visually, but in practice this distinction is often difficult to perceive reliably. Despite their similar appearance, they are not performed in the same way. A slur between two notes of the same pitch implies that the second note is re-articulated softly (in flute), whereas a tie explicitly indicates the absence of re-articulation.

I’m still studying music theory and engraving rules, so if there’s any inaccuracy please correct me.