Many older cookbooks call for filling a “refrigerator tray”. For example, in the 1960 Better Homes and Gardens Dessert Cook Book the recipe for “Banana Ice Cream” says to “Pour into refrigerator trays. Freeze till firm.” and in Anne London’s 1972 American-International Encyclopedic Cookbook, the recipe for “Refrigerator Tray Pie” says to “Pack half the crumb mixture into a refrigerator tray. Chill… Return to refrigerator to freeze.”
Doing a search for “refrigerator tray” on archive.org, I found the pamphlet for Use and Care of Your New Norge Refrigerator which mentions many uses for refrigerator trays, all involving freezing in some way. From the various recipes for ice cream and other frozen desserts on pages 31-32,
Pour into refrigerator trays and freeze.
Freeze in refrigerator tray.
…freeze in refrigerator tray until firm.
From this, I can deduce that a refrigerator tray is something that you can pour liquids into and then put into the freezer, but that’s about it.
Those pages also mention trays without the qualifier “refrigerator”:
Pour into tray of chilling unit and freeze to mush.
Pour into tray and chill to soft jelly… Return to tray and freeze to desired firmness.
Turn into freezer tray and freeze 45 minutes to 1 hour.
The list of definitions on page 9 does not include a definition for refrigerator trays, although it does include one for ice trays, and specifically mentions using them for making ice cream:
Ice Trays: Fill the trays with water to within 1/4 in. of the top. Place trays in their section on top of main freezer compartment. When making Ice Cream, use the aluminium tray by removing plastic cups or dividers.
I would guess that the ice trays mentioned are the metal trays for making ice cubes, which used to come with a removable (always metal, in my limited experience) divider that doubled as a loosening device for the ice cubes. They seem awfully small for use as a dessert pan, but then the Better Homes and Garden recipe did use the plural for its mention of refrigerator trays.