I keep writing replies that keep getting eaten by my browser and/or my own poor computing habits. (Writing posts in the browser, for starters.)
To address the original question, historically, server software wasn't considered an important distinction from regular software because there's just not all that much of it.
In addition to ASIP, the server component to PowerTalk, classic AppleShare, and a few other little things (Apple Internet Mail Server) and bundled stuff (PWS, the Sharing Control panel), there wasn't a whole lot of Mac server software.
Most of it was tools like FirstClass and other BBS or graphical BBS software, most of which were used for LANs, and then you had third party HTTP servers, most of which were designed in the days before Apple built PWS in. (There was even a Microsoft Personal Web Sharing server in the ~IE3 days.)
At the time, there was this idea that ISDN would save us all and of course in the US, there was pervasive messaging that your local Ex-Bell Telco owuld be delivering symmetric 45 megabit fiber to your house any day now. The idea of your desktop running your own web site and e-mail server made a fair bit of sense because mega-centralization onto services like Gmail hadn't happened yet, and university/work/library/free email quotas were still like... 5 megabytes at their most generous, as late as 1999 or so.
Today, massively asymmetrical connections and the general security/spam/phishing environment mean that somebody who is hosting e-mail at home is generally more likely to cause problems. Mail is still essentially computationally trivial (even Exchange will run on a NUC) but it's a lot of effort in terms of configuration/account management and patching and tracking vulnerabilities. (Depending on what method you take.)
Mail itself is fine on a slow connection(1), but many ISPs also disallow requests to 80 and 443 on home accounts, and even if you buy a small business account, there's the question of what type of site you want to run and what kind of traffic you expect(2).
... anyway.
The point being there that even when people aren't moving to centralized providers like hotmail/yahoo/gmail or even Office365, it's not very hard to see why there's movement toward VPS services for some tasks, rather than hosting on-premises.
This is an extreme digression, but it would be really interesting to see if this wouldn't have shaken down differently if ISDN didn't set the expectation for symmetric, always-on connections, and the telcos ended up being forced more enthusiastically to deliver 45/45 to every home by their promised date, which was in the late '90s. (Most contracts specified full coverage by the mid-late 2000s or early 2010s, but that kind of thing, as you know, tends to flow from city centers and new developments outward.)
(1) E-Mail is designed to be pretty resiliant. I ran it with no lost messages on a 1536/896 kilobit DSL connection that was retraining every ten minutes. I eventually called the telco to have them correct the trouble in the outside wiring.
(2) At the same time, I ran a SharePoint-based Web Site on that connection, and it was reputed to essentially be useless at the time.
To address the original question, historically, server software wasn't considered an important distinction from regular software because there's just not all that much of it.
In addition to ASIP, the server component to PowerTalk, classic AppleShare, and a few other little things (Apple Internet Mail Server) and bundled stuff (PWS, the Sharing Control panel), there wasn't a whole lot of Mac server software.
Most of it was tools like FirstClass and other BBS or graphical BBS software, most of which were used for LANs, and then you had third party HTTP servers, most of which were designed in the days before Apple built PWS in. (There was even a Microsoft Personal Web Sharing server in the ~IE3 days.)
At the time, there was this idea that ISDN would save us all and of course in the US, there was pervasive messaging that your local Ex-Bell Telco owuld be delivering symmetric 45 megabit fiber to your house any day now. The idea of your desktop running your own web site and e-mail server made a fair bit of sense because mega-centralization onto services like Gmail hadn't happened yet, and university/work/library/free email quotas were still like... 5 megabytes at their most generous, as late as 1999 or so.
Today, massively asymmetrical connections and the general security/spam/phishing environment mean that somebody who is hosting e-mail at home is generally more likely to cause problems. Mail is still essentially computationally trivial (even Exchange will run on a NUC) but it's a lot of effort in terms of configuration/account management and patching and tracking vulnerabilities. (Depending on what method you take.)
Mail itself is fine on a slow connection(1), but many ISPs also disallow requests to 80 and 443 on home accounts, and even if you buy a small business account, there's the question of what type of site you want to run and what kind of traffic you expect(2).
... anyway.
The point being there that even when people aren't moving to centralized providers like hotmail/yahoo/gmail or even Office365, it's not very hard to see why there's movement toward VPS services for some tasks, rather than hosting on-premises.
This is an extreme digression, but it would be really interesting to see if this wouldn't have shaken down differently if ISDN didn't set the expectation for symmetric, always-on connections, and the telcos ended up being forced more enthusiastically to deliver 45/45 to every home by their promised date, which was in the late '90s. (Most contracts specified full coverage by the mid-late 2000s or early 2010s, but that kind of thing, as you know, tends to flow from city centers and new developments outward.)
(1) E-Mail is designed to be pretty resiliant. I ran it with no lost messages on a 1536/896 kilobit DSL connection that was retraining every ten minutes. I eventually called the telco to have them correct the trouble in the outside wiring.
(2) At the same time, I ran a SharePoint-based Web Site on that connection, and it was reputed to essentially be useless at the time.
. I happen to be an information security analyst (MS information security, lots of DoD experience and currently working for a major bank in the PacNW), so I definitely hear you when it comes to the security aspect. 
