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; 





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.




Species of Chrysophyllum

Thanks …
chrysophyllum cainito – I suppose
I saw one more tree, but not very sure as it was too tall