How to compare 2 records of same table?

As Andre pointed out your input data seems to be incorrect. I took the liberty of changing the modified time stamps for the last two records. Now to get the results you need, first assign a sequence number based on the time stamp. Descending order will help you identify the current schedule easily. You the need to wrap it in a CTE (common table expression) and join to itself on the sequence to get the previous record:

with cte as
(
  select *, row_number() over(partition by scheduleid order by ModifiedTimeStamp desc) seq 
  from schedule
)
select curr.ScheduleID, curr.StartTime, curr.EndTime, curr.ModifiedTimeStamp,
  case
    when prev.seq is null then 'Schedule Created'
    when curr.seq = 1 then 'Current Schedule'
    else dbo.uf_GetModifiedMessage(curr.StartTime, prev.StartTime, curr.EndTime, prev.EndTime)
  end as ActionType
from cte curr
left join cte prev on curr.seq = prev.seq - 1
order by curr.ModifiedTimeStamp

To get the modified message I would prefer a function. You could do it inline but the query would be a mess:

create function dbo.uf_GetModifiedMessage(
  @currStartTime varchar(10), 
  @prevStartTime varchar(10),
  @currEndTime varchar(10), 
  @prevEndTime varchar(10)
)
returns varchar(1000)
as
begin
  declare @message varchar(1000) = NULL

  if @currStartTime <> @prevStartTime
    set @message = 'Start time modified from '+@prevStartTime+' to '+@currStartTime

  if @currEndTime <> @prevEndTime
    set @message = isnull(@message+', ','')+'End time modified from '+@prevEndTime+' to '+@currEndTime

  return @message
end

I created a fiddle[^] too, check it out.