In Canada, a certified guide is one that has successfully completed the requisite courses and exams to the standards of the Association of Canadian Mountain Guides. There are various certifications under their supervision, for instance:
ACMG Mountain Guide is the ultimate level, he/she can take you anywhere in the mountain environment be it mountaineering, rock climbing, ice climbing, hiking or ski touring. They are recognized by the UIAGM/IFMGA which is the international body recognizing the same standards. They are permitted to use their skills on any mountains in any country.
The following are also certified guides however they have limits to the type of terrain they are allowed to access as well as certain countries which will allow non-mountain guides to guide . For example in Canada:
ACMG ski guide can take you ski touring on any terrain in the winter mountain environment but is limited to ski mountaineering objectives that does not involve technical climbing. They may also lead easy glacier walks in the summer.
ACMG rock guide can guide you on any rock climb that does not involve mountaineering or glacier travel.
ACMG alpine guide can only guide mountaineering objectives that involve rock and ice but no skiing.
ACMG backpacking guide can guide single day or multi-day backpacking trips throughout the summer months in the Canadian Wilderness.
ACMG hiking guide can only lead single day hikes on marked trails in the summer.
There are apprentice levels that fall below each of these categories which must work under the direct or indirect supervision of one of the above depending on the stream.
The important thing to know is that whichever certification your guide has attained is that they have your safety as their number one priority and that is why people hire ACMG guides. They have all trained many years to get that coveted badge and are very good at what they do.