Chrysophyllum cainito (Introduced)

Chrysophyllum cainito L., Sp. Pl. 192 1753. (Syn: Cainito pomiferum Tussac; Chrysophyllum bicolor Poir.; Chrysophyllum bonplandii Klotzsch ex Miq. [Invalid]; Chrysophyllum caeruleum Jacq.; Chrysophyllum cainito var. caeruleum Jacq.; Chrysophyllum cainito var. jamaicense (Jacq.) Bois; Chrysophyllum cainito var. martinicense Pierre ex Duss; Chrysophyllum cainito var. pomiferum (Tussac) Pierre; Chrysophyllum cainito var. portoricense A.DC.; Chrysophyllum cainito var. typicum Stehlé, not validly publ.; Chrysophyllum jamaicense Jacq.; Chrysophyllum maliforme L.; Chrysophyllum monopyrenum Spreng.; Chrysophyllum ottonis Klotzsch ex Miq. [Invalid]; Chrysophyllum sericeum Salisb. [Illegitimate]);

a cultigen from C. America as per WCSP;

Belize; Cayman Is.; Colombia; Costa Rica; Cuba; Dominican Republic; Ecuador; El
Salvador; Guatemala; Guyana; Haiti; Honduras; Jamaica; Leeward Is.; Mexico
Southeast; Nicaragua; Panam; Peru; Puerto Rico; Society Is.; Southwest
Caribbean; Tonga; Trinidad-Tobago; Venezuela; Venezuelan Antilles; Windward Is as per Catalogue of life;

caimito, caimito, star apple, golden leaf tree, abiaba, pomme du lait, estrella, aguay • Marathi: Tarsiphala;

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Tree for ID 18032011-PR-2 From Chennai:

This was a slender tree with leaves that were glossy on top and had a silky sheen underneath, which was pale at first and then became a rusty colour. Is it related to the sapota?

Yes, it is Sapotaceae, Chrysophyllum cainito or Star Apple originating from America. It bears Sapota like edible fruits also.