They are based on completely different assets.
As this document states:
the government liability nominal yield curves are derived from UK gilt prices and General Collateral (GC) repo rates.
Later on, the same document defines:
A conventional gilt is a guarantee by the Government to pay the holder of the gilt a fixed cash payment (coupon) every six months until the maturity date, at which point the holder receives the final coupon payment and the principal.
These assets are usually long term. As this page states:
In recent years the Government has concentrated issuance of conventional gilts around the 5-, 10- and 30-year maturity areas, but in May 2005 the DMO issued a new 50-year maturity conventional gilt. In June 2013, following market consultation the DMO issued a new 55 year maturity conventional gilt.
Meanwhile, the document referred earlier defines "General Collateral (GC) repo rates" as:
General collateral (GC) repo rates refer to the rates for repurchase a
greements in which any gilt may be used as
collateral. Hence, GC repo rates should in principle be close to true risk-
free rates. Repo contracts are actively traded for maturities out to one year; the rates prevailing on these contracts are very similar to
the yields on comparable maturity conventional gilts.
Notice the phrase in bold. The rates are similar to comparable (e.g. 3-month T-Bills), but not identical. Unfortunately, they do not state why.
According to Bank of England definitions, the "Treasury bill tender 3 month (91 days) bills" is:
Treasury Bills are bearer Government Securities representing a charge on the Consolidated Fund of the UK issued in minimum denominations of £5,000 at a discount to their face value for any period not exceeding one year. Although they are usually issued for 3 month (91 days), on occasion they have been issued for 28 days, 63 days and 182 days. They are issued:
- by allotment to the highest bidder at a weekly (Friday) tender to a range of counterparties;
- in response to an invitation from the Debt Management Office to a range of counterparties;
- at any time to Government departments (non-marketable bills only).
Regarding why they have less data available, the same article points out that:
The secondary market in Treasury bills has in recent years become illiquid and representative rates are no longer obtainable other than those for the most recently issued 91 day bills. The rates shown are the average rates of discount at the weekly tender for 91 day bills.
Finally, regarding to which one to use, I would be definitively inclined to use the data related to the yield curve (gilts). This, as indicated above, are traded daily in the secondary market. Thus, data is more extensive, and perhaps more "reliable".