Debt to total asset ratio is simply another, equally common name for the debt ratio, calculated by dividing a company's total liabilities by its total assets to show what proportion of the company's assets are financed by creditors rather than owners. The two terms refer to the exact same calculation, interpretation, and use in financial analysis, with only the name differing depending on which textbook, analyst, or lender happens to be using it.
Why two names exist for the same ratio
"Debt ratio" is the shorter, more commonly used term in everyday financial analysis and casual conversation, while "debt to total asset ratio" is the fuller, more descriptive name that spells out exactly what is being divided by what, which some textbooks and formal credit analyses prefer for clarity, particularly when introducing the concept alongside similarly named ratios such as the debt to equity ratio. Neither name is more correct than the other; a reader encountering either term should expect the identical calculation and interpretation.
Where to go for the full explanation
See debt ratio for the complete explanation of how this measure is calculated, what counts as a reasonable level by industry, and how it compares with the debt to equity ratio in evaluating a company's financial leverage and overall risk profile.