In sheet music, can notes of a chord have different length, or how to read this sheet?

Question

I have some sheet music that I'm trying to understand, but I'm unfamiliar with the correct terminology and my understanding of it (just starting out learning music).

Specifically, the notes that are together.

I understand that this is a chord (any time two or notes are played together, it's a chord?), but I'm curious about the length of the note. The top note is a sixteenth A4, but the bottom is written as a quarter A3. Is this just a shortcut to not litter the page with a bunch of extra flags on stems? Is the A3 also a sixteenth note that's just written as a quarter note for convenience?

So would I play a sixteenth note A3/A4, release both at the same time for the rest, then an eighth note B3/B4 chord, release both for the rest, then a sixteenth note D3/D4?

Answer 1

tl;dr

When notes share the same stem, they also share the same duration.

While there are rare cases of (wrongly) written notes that seem to share the same stem while they're not, it's not your case.

Each note you see in that score shares the length of the note "above": a sixteenth, an eight and again a sixteenth, for both bars.

Some insight on stem notation

The doubt might arise, as stems height normally extend to an octave (3½ space height), which means that two voices that are an octave away can theoretically "share" the same stem.

But.

Even assuming that the notation was "wrong" as explained above, there are usually clues that can help you when you're in doubt.

In this specific case, there are three important clues.

1. only stems of notes below the middle line usually have an upper stem, so the B and D stems should be downwards, but they also should not as long as there's (theoretically) another below voice;
2. voices normally have opposed stem directions, no matter their pitch; a "higher" voice shoould always have upwards stems, and a lower voice downward stems; when using odd numbered voices, it's usually a matter of voice range and, obviously, choice; if there could be 3 or more voices for each staff, consider using more staves;
3. while, again theoretically, the first and second note could be quarter notes, the third certainly cannot: it's aligned with the last eight note, so there's not enough "time" for a quarter left since the specified time is 4/4.

Consider a (bad) writing with wrong stem direction, the upper voice using sixteenths and the lower quarters:

As you can see, the first two lower notes are quarters. The last one cannot be.

Consider that multiple voices should also have related multiple rests; that's how a real two-voice part should be in that case, assuming that the lower voice should (try to) last a quarter:

So, the part, as it's written is pretty clear: those note share the same stems, so their duration is also the same.

^{In a previous version of this answer I mistakenly confused the duration of the second note (but, for some reason, I initially wrote it right). While the suggestions about that aspect were correct, they are not in topic with the question; if you're interested in those aspect anyway, see the edit history.}

Answer 2

Musicamante gave you the answer regarding rhythm, but you also added this question...

...I understand that this is a chord (any time two or notes are played together, it's a chord?)

Many regard two tones as partial or incomplete chords. The common definition of a complete chord is three or more tones. But, in this particular case you really have the two tones just doubling at the octave. So, this...

...in terms of harmony and chords is really indistinguishable from this...

...the line without the octave doubling.

If the second notes added different pitches (pitch classes) you would get a stronger sense of incomplete chords, perhaps something like this...

So, it's a case of octave doubling versus incomplete chords.