How do people differentiate between EF and "repair & replacement fund"?
We just call it Cash Reserves, it is unassigned, non-budgeted, unlabeled for whatever purpose we may need.
Basically, 3k that has no defined bucket. It doesn't materialize until the last few months of the year, and if used is OK. If not most likely gets dumped into taxable accounts, vacations, or purchases we otherwise put off and finally decide we want.
I also don't differentiate between emergency fund and repair/replace fund.
I tend to see it as a spectrum of possible responses to unexpected expenses or expected expenses that occur at unpredictable times. The greater the expense or emergency, the further you move up the level of response:
First, use cash flow from current income to cover the smaller-but-still-significant unexpected expenses. It may mean that I save less this month than I would otherwise save but it does not decrease the value of my savings account. The beauty of a mustachian lifestyle is that this first line of defense will cover quite a lot more than the average spendypants' current cashflow even without tightening your belt.
Second, maintain cash reserves in an amount appropriate for your circumstances to pay for the larger unexpected expenses. I used mine this summer to replace our home's air conditioner. I would also put car repair / replacement in this category. This line of defense is particularly important for emergencies that include a loss of income. The closer you get to FI, the less money you need here because you can rely more on passive income.
Third, responsibly use credit to buy time. A HELOC, a low-interest car loan, or low/no interest credit cards could be enough to spread out a larger expense to pay it off with current income or to liquidate other assets. This response is less appropriate for emergencies accompanied by loss of income. Use the time you buy to look for alternative means of support, including disability insurance claims, social security disability income, help from family or friends, etc.
Fourth, liquidate investments that generate little or no tax consequence. Realizing a loss in a taxable account is best. Next is appreciated assets in taxable accounts or contributions to a Roth IRA (prior to age 59 and a half). When you are in this territory, it is a pretty significant emergency.
Fifth, if you are truly desperate, you can liquidate assets that create bad tax consequences. You don't want to go here if at all possible.
Of course, you should also be prepared to slash expenses in proportion to the severity of your emergency.