What's the difference between Zinc Ascorbate and Zinc Gluconate?
As I understand your question, “the two” refers to Zinc Gluconate and Zinc Ascorbate.
Zinc gluconate and zinc ascorbate are distinctly different compounds.  They are both adducts of Zn with one Zn and two bidentate oxygen-based ligands of organic acids.  Some basic information from PubChem for both zinc gluconate and zinc ascorbate is given below.
Zinc gluconate: $\ce{C12H22O14Zn}$
Zinc gluconate [Gluconic Acid Zinc (II) Salt] is a zinc salt of gluconic acid comprised of two gluconic acid molecules for each zinc cation ($\ce{Zn^2+}$). Zinc gluconate is a generally recognized as safe (GRAS) substance by FDA.

Of interest, as related to periodontic issues note that a phase 4 clinical trial was completed 2014-12-16 “The effect of Zinc-D-gluconate on bleeding propensity of the periodontium in patients with chronic parodontitis - a randomised, placebo-controlled, double-blind interventional study”.
Zinc ascorbate: $\ce{C12H14O12Zn}$
Zinc ascorbate is a zinc salt of ascorbic acid[Vitamin C] comprised of two ascorbic acid molecules for each zinc cation ($\ce{Zn^2+}$). Zinc ascorbate goes by a variety of different names, L-Ascorbic acid, zinc salt (2:1), L-Ascorbic acid, zinc salt, (-)-Ascorbic acid, zinc salt to name a few.

A ResearchGate reference discusses zinc-gluconate, taurine in reducing halitosis and gingivitis.  A portion of the abstract follows:

Objectives: to evaluate the efficacy in reducing halitosis and gingivitis insurgence in fixed orthodontic patients of a
zinc-gluconate, taurine and cetylpyridinium-chloride (CPC) oral-rinse,
sole or combined with a toothpaste with the same active principles.

References:

https://pubchem.ncbi.nlm.nih.gov/compound/443445
https://pubchem.ncbi.nlm.nih.gov/compound/Zinc-ascorbate#section=Structures
Dalessandri, Michela &amp; Dalessandri, Domenico. (2011). Halitosis And Gingivitis Reduction Using A Zinc-gluconate-taurine-cetylpyridinium-chloride Oral-rinse And Toothpaste. (link)