Differences in clinch clamps

The commonly available tools for attaching clinch clamps to PEX fittings have compound leverage. (e.g. https://www.amazon.com/EFIELD-Clamps...1&s=hi&sr=1-29 )

I also see clinch clamps sold with a tools that don't have compound leverage. (e.g. https://www.amazon.com/Seloky-130Pcs...xpY2s9dHJ1ZQ==)

Are the clinch clamps for PEX a different type of clamp than the "hose clamps" sold with the latter type of tool?

Short answer: yes. Your second link is for clinch type hose clamps, not PEX clamps. For use with rubber or vinyl hose or the like, not PEX.