Hi, To my knowledge, there is no difference in meaning here. The verb 'start' can be followed either by a to-infinitive or -ing form (gerund). A good E-E dictionary can provide you with detailed information on what can follow certain verbs.
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Often there is no or minimal difference, but not always. He started to eat his meat after I told him that it wasn't squirrel. vs. He was a vegetarian but recently he started eating meat. While they MAY be interchangeable, in these examples there are clear preferences
The difference is one of direction. Verbs that can be followed by either -ing or to, refer to past or future action.
I will remember to tell him TOMORROW that . . . .
I remember telling him YESTERDAY that . . . .
Cheers!