** In practice, the same formula, as you say is used for both series and parallel resonance LC circuits. However when such circuits contain significant resistance, there is a resonant formula which includes this R as well as the L and C, for parallel circuits only.. The result of using the LCR formula compared to the LC formula, produces a frequency difference which would be exceeded by the variation due to the tolerance of the L and C components. For that practical reason the LCR formula is seldom used. The R is considered as being in series with L, with C in parallel with the LR series combination. Bandwidth, Q, Impedence, and Power Losses are other factors of concern in such circuits. See both formula and circuits, re the above at my LINK.