The doofuses in the auto parts store know nothing. I'll bet that just about every grease they sell is lithium or lithium complex base grease.
Grease has four parts:
Base or thickener...this is a chemical "soap" that is something like a sponge. It holds the oil that does the actual lubrication. Lithium and lithium complex are the most common thickeners.
Oil...it can be conventional oil, or synthetic oil, or a blend of the two.
Solid additives...molybdenum disulphide, graphite, Teflon (OK in grease, no-no in engine oil)
Other stuff...tackifiers, dye, extreme pressure agents, etc.
NLGI #2 means National Lubricating Grease Institute (no connection to the National Frying Grease Institute), and #2 consistency...#3 is thicker, #1 is thinner, #0000 is nearly liquid.
So...whether the grease has synthetic oil or not means nothing to the base. Read the tubes. You'll find that most tell you what the base (thickener) is made of, and most of those will be lithium or lithium complex.
Many of us use moly grease in all the grease fittings on our Toyotas with good results. You can use the two types if you wish, no problem.
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Rooster today;
Feather duster tomorrow.