The substrate in both reactions is isobutyl bromide, $(\text{CH}_3)_2\text{CHCH}_2\text{Br}$, which is a primary ($1^\circ$) alkyl halide. Primary alkyl halides undergo nucleophilic substitution predominantly via the $S_N2$ mechanism because the corresponding primary carbocation required for an $S_N1$ reaction is highly unstable . Furthermore, if an $S_N1$ mechanism were to occur, the primary carbocation would undergo a hydride shift to form a more stable tertiary carbocation, leading to a rearranged product. Since the given product in both cases is the unrearranged ether (isobutyl ethyl ether), it confirms that no carbocation intermediate is formed. Therefore, both reactions proceed via the $S_N2$ mechanism, irrespective of whether the attacking nucleophile is neutral ($\text{C}_2\text{H}_5\text{OH}$) or a strong anionic nucleophile ($\text{C}_2\text{H}_5\text{O}^-$).