A deposit is taken before work begins. Progress payments are taken at agreed points during it.
What they solve
On any job where material and labour are spent before the invoice is settled, the business is funding the customer's work out of its own cash — see working capital.
The longer and larger the job, the more of it is being financed, and the more a single non-payment costs.
Deposits
Commonly enough to cover the materials that must be bought before work can start, so the business is not out of pocket at any point.
Beyond the cash, a deposit is a filter. A customer unwilling to commit anything is the customer most likely to become bad debt.
Progress payments
For work spanning weeks, payment staged against defined milestones rather than a single invoice at the end.
The milestone has to be objective — a stage completed, an inspection passed — rather than a date or a percentage of effort, or it becomes an argument at each stage.
It is not revenue when it arrives
Money received for work not yet done is deferred revenue, a liability until the work is performed.
Treating deposits as income makes a business look more profitable than it is, and the correction arrives when the work has to be delivered against money already spent.
Where a portion is held back
On construction work a percentage is frequently retained until completion and sign-off — see retainage. It is earned revenue that is not yet collectable, and it needs tracking separately or it is quietly forgotten.
Setting them
Deposit levels are constrained by law in some jurisdictions and trades, particularly in home improvement. Worth confirming locally before setting a policy.