I assume the question is, "Can you tell, from appearance, whether the script is Sinhalese vs. Kannada?" (or other languages). No, because scripts can be and often are employed non-traditionally in writing languages other than the language typically associated with the script (Zulu and Somali are written in ordinary Latin letters). But to the extent that a certain script is associated with a particular language, you can make a reasonable guess about a language based on script. Ethiopic script is used to write quite a number of languages, and careful analysis of what letter-shapes are employed may tell you that a text is in Bilen, because it uses the letter ⶓ. Likewise, Mongolian (Cyrullic) and Russian can be distinguished by the presence of ө and ү (which are used in other languages, so it may not distinguish Mongolian from all other languages).
Linguistic classification focuses on functional taxonomy and historical origin. Knowing that a script is an "abjab", "abugida", "syllabary" etc. is of little help in language identification. Knowing that a script is historically "Semitic" vs. "Sinitic" likewise does not narrow down the possibilities in any useful way.
The best way to understand the diversity of letter shapes in a historically-unified set of writing systems would be to look at the various Brahmic scripts, used to write languages of India and vast numbers of language in places influenced by India (Tibetan, Java, Mongolia, SE Asia). On the practical front, that particular page probably does not help because of computer font problems. The scripts for Odia, Tamil, Kannada, Malayalam, Telugu, Sinhalese are all visually quite similar, but you might develop a heuristic for distinguishing Tamil தமிழ் அரிச்சுவடி from Sinhalese සිංහල අක්ෂර මාලාව (Tamil has a much higher percentage of horizontal and vertical straight strokes). Thai อักษรไทย, Khmer អក្សរខ្មែរ, Burmese မြန်မာအက္ခရာ and Georgian მხედრული are probably ultimately related historically (the history of Georgian script is unclear), but one might easily confuse Burmese and Georgian based solely on superficial appearance.
This web page leads to a number of useful help-tools for scripts, and the Omniglot website is probably most used by linguists, but they all require you to have some basic classification. The Wikipedia language recognition chart could be useful for getting an initial clue as to what the possible candidates are. This article moves in the direction of devising general computational tools for talking about script shapes which might eventually lead to a computational method of determining what script one is faced with (not relying on the shortcut of finding that ஞ் is U+0B9E which is called "Tamil Letter Nya", telling you that it is Tamil, unless it is another language written in that script).