I was taught at an institution I study in that using $\ce{K2Cr2O7}$ in the presence of $\operatorname{dil}.\ce{H2SO4}$ will oxidise $1^{\circ}$ alcohols to aldehydes, and $2^{\circ}$ alcohols to ketones. This is supported in here too.
At the same time, I came across Jones reagent ($\ce{Na2Cr2O7}$ in the presence of $\operatorname{dil}.\ce{H2SO4}$) on Khan Academy. But this says that it is an extremely strong oxidising agent and can oxidise Aldehydes to Carboxylic Acids too (thus giving acids on the oxidation of $1^{\circ}$ alcohols).
I do not understand how the above two reagents have different oxidising abilities. Is my premise itself wrong or is there any reason for it to have different oxidising abilities?