The simplest answer is 'a small pinnace or a barque.' However, both words cover a rather significant variety of vessels in size and capability, especially in the 16th century; barque in particular is confusing because at that time the later distinguishing features of barques, the rig, didn't yet exist. The Spanish Armada included a number of ships labeled pinaza carrying one gun, but we don't have any dimensions attached to them. English pinnaces opposing them (of the larger type--the smaller type was often a ship's boat, but I'm not finding consistent numbers for displacement) had around 4 to 6, and might have been around 100 tons. The more mysterious classic barque, whatever it actually was, seems to have been closer to your tonnage range for a seaworthy vessel. They were shallow-draught, maybe eight feet or so.
The size issue for a 40-ton vessel is no small matter, either. Even the relatively tiny Golden Hinde of Sir Francis Drake was under 300 tons loaded; the mighty HMS Ark Royal wasn't even 700. I've always been a bit oddly skeptical of Cavendish having a 120-ton ship with 18 guns of any serious weight, or a ship half that size with eight or ten. In a quick dig, illustrations of a 50-ton 'barque' of the pre-rig era seem to favor artists' interpretations of Le Griffon, famous for being the first ship of European design known to rest at the bottom of the Great Lakes. There are one or two other mentions in New World warfare of the late 1500s (notably the battles over Fort Caroline / San Mateo in the late 1560s) as well of such ships in English employ--Hakluyt, I think talks about them?--but frustratingly little hard data or description. Perhaps /u/jschooltiger has his books to hand and can clarify some of this, but I've never been entirely clear about the affinities and capabilities of anything under about 100 tons.
[edit: Johnstone's 1831 Lives and Voyages of Drake, Cavendish, and Dampier refers to Hugh Gallant as a 'light bark' on page 174, and notes that Drake also preferred such small and fleet vessels at various points, ranging reputedly from about 25 to 80 tons--a huge span. Hakluyt also calls it a 'barke' but without further comment on just what that meant. Given the discussion of armament for other vessels, one can reasonably consider it unarmed except for its complement.]
Thanks for the ping u/khosikulu. Unfortunately my resources on this are at work/the university, and I am not (Happy Spring Break!), but one thing that I would consider is whether the 40 tons is tons burthen (most likely for this type of ship) rather than tons displacement. Tons burthen was a usual way of measuring ship size in the Middle Ages, and was basically meant to be a rough measure of internal volume.
That said, I cannot offer anything useful as to the type of vessel until I can get to my books. Please ping me in a week or two u/maijax18 if I don't remember to get back to it.