More or less. In a defined benefit pension scheme, a member's pension is calculated (defined) as a percentage of his salary - typically that in the last year of employment or an average over his entire length of service. He may pay a fixed percentage of his salary (or perhaps nothing at all) and the employer pays the rest. All the money goes into one big pot from which the pensions are paid. The employer takes the investment risk.
Periodically a valuation is carried out by the scheme's actuary to see if what is in the pot plus what is being paid in will be sufficient to meet the promised benefits. If its insufficient the scheme is said to be in deficit, if there's more than enough it's in surplus.
Being in deficit isn't necessarily a problem unless the employer cannot afford to increase its contributions without risking the viability of the company ('our machines have worn out and we can't afford to replace them as we have to top up the pension fund').
Just to make life more interesting, the assumptions used to calculate the deficit/ surplus can make a big difference and are changed from time to time and previous Governments have unexpectedly raised taxes on pension funds and stopped them carrying forward surpluses to see them through the bad times.
In a defined contribution scheme, the employee and employer pay in an agreed amount which is invested and when the employee retires normally the investments are sold and an annuity purchased. This turns the lump sum into a guaranteed income for life. If investments haven't done as well as hoped or the terms for purchasing annuities are worse than expected the amount of pension will be disappointing but that's not a defecit as no promises were made. The employee takes the investment risk.
Endowment policies were not pensions. They were typically sold to pay off mortgages and you could either choose one which was guaranteed to pay what you owed at the end of the mortgage term or one which guaranteed less but had a share of the insurance company's profits which it was hoped would provide enough. The latter was cheaper but the policyholder took some of the investment risk. In some cases investments didn't do as well as had been assumed and people found they had to find extra money to pay off their mortgages.
Equitable Life is interesting in that it made promises to some policyholders but did not make investments to enable it to meet those promises. As a mutual organisation owned by its members/policyholders it had no option but to 'rob Peter to pay Paul' and long arguments ensued about how the assets should be shared out.