These two terms get used as if they mean the same thing, but depending on the country, they can refer to genuinely different documents.
The general distinction
A student visa is typically the document that allows you to enter a country. A study permit (where the distinction applies, such as in Canada) is a separate authorization that allows you to actually study there once you have arrived. In some cases you need both; in others, one covers the function of the other.
Canada is the clearest example
In Canada, most applicants need a study permit to study, and separately may need a temporary resident visa or an Electronic Travel Authorization to enter the country, depending on nationality. It is possible to have one without realizing you also need the other.
The UK and US use a single-document model
In the UK, the Student visa itself covers both entry and permission to study. In the US, the F-1 student visa serves a similar combined function, paired with the I-20 form issued by your school.
Why this distinction actually matters
Assuming your visa alone covers everything, when a separate permit is actually required, is a common and entirely avoidable source of delay. Before you travel, it is worth confirming exactly which documents your specific destination requires — the terminology alone is not a reliable guide.