ties and slurs

Ties connect exactly two (adjacent) notes of the same pitch
Slurs connect 2 or more chords (with one or more note) of any pitch

Slurs connecting two (adjacent) notes of the same pitch are pretty hard to tell from Ties from looking at them, but if you change the pitch of one note and the other follows, it is a tie

The standard reference most people cite these days is Elaine Gould's "Behind Bars", but there are several other excellent older books as well. Plus you can learn a lot carefully studying existing scores from a variety of publishers.

There are many reasons why the engraving rules for ties differ from slurs. One is, ties are nearly always horizontal because they connect notes of the same pitch, whereas slurs are very often angled to follow the contour of the line and thus will need to attach differently. Also because ties connect adjacent notes, they are normally quite short, but slurs can get quite long, and the engraving rules are designed to keep them from getting out of hand. Also ties can exist within slurs and thus need to tuck inside. Also, because short slurs can look at first like ties, anything that can be done to accentuate the difference helps the eye understand what it is seeing. It's quite unfortunate someone hundreds of years ago decided to use such similar-looking symbols for these two very different concepts, so we do what we can to minimize the confusion.

Although you didn't attach a score so I can't say what specific slur you mean by wondering about, one reason slurs sometimes end along the stem is to avoid too steep an angle which would take too much space on the page. Again, ties won't have that issue because they are normally horizontal.