  We compare correlators for pseudoscalar and vector mesons made from valence
strange quarks using the clover quark and highly improved staggered quark
(HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to
normalise vector and axial vector current operators made from HISQ quarks,
clover quarks and from combining HISQ and clover fields. This allows us to test
expectations for the renormalisation factors based on perturbative QCD, with
implications for the error budget of lattice QCD calculations of the matrix
elements of clover-staggered $b$-light weak currents, as well as further HISQ
calculations of the hadronic vacuum polarisation. We also compare the approach
to the (same) continuum limit in clover and HISQ formalisms for the mass and
decay constant of the $\phi$ meson. Our final results for these parameters,
using single-meson correlators and neglecting quark-line disconnected diagrams
are: $m_{\phi} =$ 1.023(6) GeV and $f_{\phi} = $ 0.238(3) GeV in good agreement
with experiment. The results come from calculations in the HISQ formalism using
gluon fields that include the effect of $u$, $d$, $s$ and $c$ quarks in the sea
with three lattice spacing values and $m_{u/d}$ values going down to the
physical point.
