Why do the DTFT and FFT give me completely different results for magnitude at a specific frequency?
HINT:
Try introducing the sampling frequency $F_s$. Then $f$ in the relation in Equation $(1)$ is relative to the sampling frequency
$$
\omega = 2\pi f\quad\text{where}\quad f = \frac FF_s\tag{1}
$$
Where the units are as follows:

$\omega$ in [radians/sample]
$f$ in [cycles/sample]
$F_s$ in [samples/second]
$F$ in [cycles/second] or [Hz]

Your discrete time vector for your signal should be as shown in equation $(2)$
$$
t = nT_s\quad\text{where}\quad T_s = \frac 1F_s\quad\text{and}\quad n = 0, \ldots, N - 1\tag{2}
$$
You seem to use the frequency $F$ in [Hz] instead of the relative frequency $f$ in [cycles/sample].