In common questions on thermodynamic processes, say for example a simple straight-forward question like "A gas at $T_1\ K$ and $P_1$ atm is suddenly released at atmospheric pressure. Find the final temperature of the gas", we assume the process to be adiabatic since no heat is exchanged between the system and the surroundings in that small interval of time. So my question is, do all quick processes have to be adiabatic, and similarly, is a slow process always isothermal?
If a process is rapid enough that there is little heat transfer between system and surroundings then treating it as adiabatic serves as a good first approximation (an adiabatic process strictly requires zero heat transfer). For example this approximation is employed in calculating sound speed through a medium, because contraction-expansion cycle of the medium due to passage of acoustic wave is considered rapid. Ultimately whether such an approximation is good enough is verified only by doing experiments.
A slow process on the other hand approximates a quasistatic process. A quasistatic process is one in which the system passes through a succession of equilibrium states while executing a process. A quasistatic process can be isothermal if the process involves maintaining constant temperature, but is not limited to it.
Adiabatic means “without heat”. You can have quick processes either with (gas combustion) or without (Joule expansion) heat transfer.
Isothermal means “same temperature”. You can have slow processed that preserve temperature (ice melting in water; slow expansion while connected to a heat reservoir) or don’t (adiabatic expansion i.e. of rising air)