We present characterizations of the Besov-type spaces <svg style="vertical-align:-4.27347pt;width:25.4px;" id="M1" height="17.450001" version="1.1" viewBox="0 0 25.4 17.450001" width="25.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.45)"> <g transform="translate(72,-58.04)"> <text transform="matrix(1,0,0,-1,-71.95,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0">𝐵</tspan> </text> <text transform="matrix(1,0,0,-1,-62.75,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0">,</tspan> <tspan style="font-size: 8.75px; " x="6.0388799" y="0">𝜏</tspan> <tspan style="font-size: 8.75px; " x="-0.5" y="8.3900003">𝑝</tspan> <tspan style="font-size: 8.75px; " x="3.7797279" y="8.3900003">,</tspan> <tspan style="font-size: 8.75px; " x="5.9677281" y="8.3900003">𝑞</tspan> </text> </g> </g> </svg> and the Triebel-Lizorkin-type spaces <svg style="vertical-align:-4.27347pt;width:25.825001px;" id="M2" height="17.450001" version="1.1" viewBox="0 0 25.825001 17.450001" width="25.825001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.45)"> <g transform="translate(72,-58.04)"> <text transform="matrix(1,0,0,-1,-71.95,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0">𝐹</tspan> </text> <text transform="matrix(1,0,0,-1,-62.41,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0">𝑠</tspan> <tspan style="font-size: 8.75px; " x="3.8508799" y="0">,</tspan> <tspan style="font-size: 8.75px; " x="6.0388799" y="0">𝜏</tspan> <tspan style="font-size: 8.75px; " x="-1.8099999" y="8.3900003">𝑝</tspan> <tspan style="font-size: 8.75px; " x="2.469728" y="8.3900003">,</tspan> <tspan style="font-size: 8.75px; " x="4.6577282" y="8.3900003">𝑞</tspan> </text> </g> </g> </svg> by differences. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking <svg style="vertical-align:-0.17555pt;width:35.325001px;" id="M3" height="10.9125" version="1.1" viewBox="0 0 35.325001 10.9125" width="35.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan> <tspan style="font-size: 12.50px; " x="9.8648672" y="0">=</tspan> <tspan style="font-size: 12.50px; " x="21.905256" y="0">0</tspan> </text> </g> </g> </svg>.