A little more information on your engraved gun. It appears to be a Llama XVI. It is a second tier variation / upgrade from the Llama III-A. It is functionally identical to the Llama III-A except for caliber. Here are a few excerpts from a notable Llama web page.
Llama III-A
Manufactured from 1954 to 1997. Self-loading pistol, blowback operation (earlier models up to about 1975: locked breech), miniature copy of Colt 1911 in 9 mm corto/.380 ACP with seven-round magazine and with grip safety. Also fitted with longer manual safety lever. Early models fitted with lanyard ring; later models replaced this with a ventilated rib and plastic target grips. Luxury finishes (including gold plating) and various engraving options were available. One of the most successful models in the Llama range.
Llama XV "Especial"
Manufactured from 1954 to 1997. Self-loading pistol, blowback operation, miniature copy of Colt 1911 in .22 LR with grip safety. Identical to Llama III-A except for calibre.
Llama XVI
Manufactured from 1954 to 1997. Self-loading pistol, blowback operation, miniature copy of Colt 1911 in .22 LR with grip safety. Identical to Llama XV except for luxury finish (including gold plating) and various engraving options.
Your second gun looks like Llama Minimax-II. I know that the Llama brand has been crafting .38 Super guns out of the Philippines the past few years. The original manufacturer, Gabilondo y Cia. Vitoria went bankrupt in 1992. Being a 1998 production gun, it falls into the production of some new owner that I haven't spent the time to research. There were many changes of hands between 1992 and 1998 when the original succession of Spanish owners went under.
Obviously the Llama name has been recently sold off and production out of the Philippines has "resurrected" the brand, although the newer guns I have seen have all been .38 Super and fall into the 1911 clone design.
Hope this helps.