Evolution is a troublesome word. I believe in evolution too if it only means a gradual change of form, or such change of anything. But I think the word Evolutionism includes the meaning of changing life from from one species to another species (or from "family" to family? I could never get that clear to me).
You are hitting on two of the reasons there is so much confusion about evolution.
First "gradual change of form" vs. "changing from one species to another".
Yes, evolution includes both. But note that it is not limited to "changing from one species to another". It also includes "gradual change of form".
Many people mistakenly dismiss the gradual change of form as "not evolution". But it is evolution, and it is the gradual change of form that may lead to new species. In short, you can get gradual change of form without new species. But you also get new species through gradual change of form.
After all, if you keep gradually changing the form, you eventually arrive at something different enough from the original form that it can properly be called a new species.
So gradual change of form and changing to a new species are tied together as cause and effect. The gradual change of form is the cause, and one possible effect of that change is a new species.
Second, changing from one species to another vs. one family to another.
Evolution is always, always, always about changing from one species to another. (And always to a new species that did not exist before. You don't get a change from one existing species to another existing species.)
Are you familiar with the Linnean classification of life forms? It is not used as rigidly as it used to be, but it starts with the basic unit of species, groups similar species into genera, then similar genera into families, similar families into orders, similar orders into classes, similar classes into phyla and similar phyla into kingdoms such as the plant kingdom, the fungus kingdom, the animal kingdom.
You needn't memorize that list. The important thing is that every classification above species is simply a larger and larger group of species. These classifications have been devised by scientists for the purpose of easy reference to particular species and groups of species.
Nature knows nothing of the dividing lines biologists impose on life forms for the purpose of classification. No more than light rays know of the human classification of wave frequencies into colours.
The only distinction between life forms that exists in nature is the species---and even that distinction is not always clear at times.
So evolution is always about change in species and the development of new species. Because that is the only place in nature where evolution can happen.
You can never get direct evolution from one family to another or one order to another.
And here lies the problem. Most non-scientists know plants and animals by common names that do not correspond to scientific species names. Common names correlate more closely to higher taxonomic categories like family and order which are actually groups of similar species.
So when a non-scientist wants to see evolution producing new species, they are thinking of something like a hippo becoming a horse. Not possible, because these are species in different groups of species and evolution can never plop a new species into a different group than its immediate ancestor.
What can happen and what biologists believe did happen is that at one point there was a species which was ancestral to both groups. The species split into two separated populations, and each population continued to gradually change form as all species do.
However, each population changed in different ways and kept changing in different ways. Well, you know what happens if you come to a fork in the road and you take one way and your friend takes another way. You end up at very different destinations. So over time, one population became horses and the other populations became hippos.
Note that this does not mean that horses became hippos. Nor does it mean that hippos became horses. Rather it means that some descendants of the ancestral species became horses and other descendants of the ancestral species became hippos.
This is called "cladistic" (branching) speciation, and is the most common type of speciation, though there are others as well.
The problem with most anti-evolution thinking is that it is linear--trying to follow a straight line from one kind of life form to another. However, it tries to follow from the tip of one branch to the tip of another branch.
The only way to connect branches is not from tip to tip, but by tracing each branch back to the larger branch they are growing from. It is only at the common point of origin that the two branches touch each other. Once they have separated there is no way a new twig on one branch can produce a leaf on the other branch.
So all new species are new to the group the ancestor is already part of. They are never new additions to a different family or order or class. Nor are they ever a transition between families or orders or classes that were established in the past.
The only place you can have a transition between orders or families or any classification higher than species is at the point of common origin of the two groups when only a single species existed. And the descendants of that species divurged and multiplied more new species until the two divergent groups became identified as belonging to different orders or families or whatever, after the fact.
This is one of the characteristics about evolution that make it testable. If you have reason to believe that two groups have a common origin, you can make predictions about what the common ancestor looked like, when it lived and what changes had to occur in each descendant group to get to the characteristics of the living descendants.
Then you can check to see if the fossil record shows the sort of animals that must have existed in the transitional period, with the right sort of characteristics and in the right time frame. So far, we have not found a fossil that seriously compromises the evolutionary scenario.