More or less. Glashow produced an early blueprint in 1961 before the Higgs mechanism was worked out, unaware of it Salam and Ward reproduced it in 1964. Weinberg and Salam presented the final theory independently in 1967. However, they knew each other well, and collaborated on some papers since 1962, so were likely aware of each other's thinking. After a key experimental confirmation in 1973 the Nobel prize was awarded in 1979, Ward was left out.
Kibble has helpful notes on History of Electroweak Symmetry Breaking, based, in part, on personal recollections. Here are the relevant parts:
"Glashow (1961) proposed a model with symmetry group $SU(2)\times U(1)$ and a fourth gauge boson $Z^0$, showing that the parity problem could be solved by a mixing between the two neutral gauge bosons. Salam and Ward (1964), unaware of Glashow's work, proposed a similar model, also based on $SU(2)\times U(1)$. Salam was convinced that a unified theory must be a gauge theory... But in all these models symmetry breaking, giving the $W$ bosons masses, had to be inserted by hand — spin-$1$ bosons with explicit mass were known to be non-renormalizable.
[...] By 1964 both the [Higgs] mechanism and Glashow’s (and Salam and Ward’s) $SU(2)\times U(1)$ model were in place, but it still took three more years to put the two together. Unified model of weak and electromagnetic interactions of leptons proposed by Weinberg (1967) — essentially the same model was presented independently by Salam in lectures at IC in autumn of 1967 and published in a Nobel symposium in 1968 — he called it the electroweak theory.
[...] Salam and Weinberg speculated that their theory was
renormalizable. This was proved by Gerard ’t Hooft in 1971 — a tour de force
using methods of his supervisor, Tini Veltman, especially Schoonschip. In 1973 the key prediction of the theory, the existence of neutral current interactions — those mediated by $Z^0$ — was confirmed at CERN. This led to the Nobel Prize for Glashow, Salam & Weinberg in 1979 — but Ward was left out (because of the ‘rule of three’?). ’t Hooft and Veltman gained their Nobel Prizes in 1999. In 1983 the $W$ and $Z$ particles were discovered at CERN."